[Andrew:] Regur regurgitate-arianism you watch.
[Suzanne:] Can't find it.
[Andrew:] . They're probably looked out or something the key.
[Suzanne:] Well.
[Andrew:] Hello, hiya,. Don't do phone calls. made your. International Longmans Dictionary.
[Suzanne:] Really got a thing really. [LAUGHTER] Have any?
[Andrew:] I think actually ask them.
[Suzanne:] Oh, I see.
[Andrew:] Oh we've been.
[Suzanne:] [LAUGHTER]
[Andrew:] What with the mileage.
[Suzanne:] Yeah. Yes.
[Andrew:] Right.
[Suzanne:] Mm. Oh.
[Andrew:] [LAUGHTER]
[Suzanne:] Yeah that, that's where you.
[Andrew:] Mm.
[Suzanne:] gonna ring then cos I'm, I'm not staying like this. Oh alright then,.
[Andrew:] Oh sorry.
[Suzanne:] What? That tiggles.
[Andrew:] Tiggles?
[Suzanne:] Yeah, what else.
[Andrew:] Tickles, not tiggles.
[Suzanne:] [LAUGHTER]
[Andrew:] It's C, K.
[Suzanne:] Alright.
[Andrew:] Not G, tickles.
[Suzanne:] Yeah, it's very flash then. [LAUGHTER] Yeah..
[Andrew:] What? Have a nice three piece suite for you. Take it...
[Suzanne:] Not
[Andrew:] Lucky oh,. Sean Connery? That on there, see?
[Suzanne:] Mhm.
[Andrew:] Good. [strange clucking noise]
[Suzanne:] Come through. That's disgusting.
[Andrew:] [LAUGHTER] Why? [LAUGHTER]
[Suzanne:] [LAUGHTER] Right.
[Andrew:] Yeah it'll have to be count.
[Suzanne:] [LAUGHTER]
[Andrew:] It's out of order.
[Suzanne:] Yeah, I know.
[Andrew:] Get on to.
[Suzanne:] [LAUGHTER]
[Andrew:] I'm gonna grow erm, because I could
[Suzanne:] Yeah, she's got eyes like, she.
[Andrew:] Did she? Woman. I.
[Suzanne:] It's covered.
[Andrew:] I meant cut the erm,.
[Suzanne:] So I've given you five.
[Andrew:] Think you can alright?
[Suzanne:] Yeah.
[Andrew:] Yeah I'll get around to it.
[Suzanne:] Darling.
[Andrew:] I will, honest... You.
[Suzanne:] I.
[Andrew:] Hi Eric.
[Suzanne:] Yeah.
[Andrew:] Nor for the fun of like.
[Suzanne:] [LAUGHTER]
[Andrew:] [LAUGHTER]
[Suzanne:] I have.
[Andrew:] Mm. Right. What is it I. It's dark and.
[Suzanne:] No. [LAUGHTER]
[Andrew:] It.
[Suzanne:] chance to see him in.
[Andrew:] Erm, actually he's darker than, it's yellow.
[Suzanne:] Mm.
[Andrew:] . It's yellow. No, it's me doing that not someone else.
[Suzanne:] What? [LAUGHTER]
[Andrew:] Nothing.
[Suzanne:] Oh.
[Andrew:] Sorry eh.
[Suzanne:] What?
[Andrew:] . I'm not gonna shave that for three weeks.
[Suzanne:] That'll look nice.
[Andrew:] No that, that is right really threatening.
[Suzanne:] Yes. [LAUGHTER]
[Andrew:] Think you're hard?
[Suzanne:] [LAUGHTER] oh my god.
[Andrew:] Well hard. That was well funny last time, you see me in a room, we're playing er games. I, I say a word
[Suzanne:] Yeah.
[Andrew:] and, and you, you have to say another word that sounds like it.
[Suzanne:] Yeah.
[Andrew:] And eh, like I, if I say loverks
[Suzanne:] Mm.
[Andrew:] You say bloverks, souverks,.
[Suzanne:] proper words.
[Andrew:] No you, we're doing it, well this a large.
[Suzanne:] Mm. Mm, can't imagine this.
[Andrew:] You has to come down.
[Suzanne:] It's really funny, oh.
[Andrew:] When we were in the room it smelled, cos Si, Dave, Jolly.
[Suzanne:] Mm.
[Andrew:] , Colin, someone else, Johnny. There's her poxy car keys.... Is he alright there?
[Suzanne:] Yeah.
[Andrew:] Right...
[Sanjay:] I've taken her out to lunch.
[Andrew:] Yes, right.
[Sanjay:] What's that?
[Val:] Dunno. I tried to get one yesterday,.
[Sanjay:] Eh?
[Val:] I chance to.
[Sanjay:] Where'd you try? Down the road I think.
[Val:] Sainsbury's.
[Sanjay:] You might
[Val:] I didn't think you'll mind having scrambled eggs with toast anyway.
[Sanjay:] Lovey dovey,.
[Val:] You get more eggs this way, you get two eggs this way. [LAUGHTER]
[Sanjay:] , preferred the other way.
[Val:] Not that.
[Sanjay:] Yeah, but you're only giving us the...
[Val:] . If you always feel hungry what is the point?
[Sanjay:] What diet?
[Val:] She's lost two and a half stone within about two or three months.
[Sanjay:] Ha, what diet's she on?
[Val:] Yeah, she works on this special diet plan, special diet and what have you. I said well how do you manage to keep the weight off? Well she said I've done a bit. Why no I've never seen you two
[Sanjay:] She is, she is jealous at having a dig at her.
[Val:] No, no, I won't, I'm, I'm
[Sanjay:] Pretty cold.
[Val:] If, if she had believed the aim to keep it off, I would've been jealous, but she, she's not going to find it easy to keep her weight, she's out here when she's put back on pound. [LAUGHTER]
[Sanjay:] She's tried. What says you're.
[Andrew:] Yeah so am I.
[Val:] Pardon?
[Andrew:] So am I what I've left off.
[Val:] Well I don't know.
[Andrew:] It's all that work you do, cut the lawn.
[Val:] [LAUGHTER]
[Andrew:] And. Right that's all.
[Val:] That one is.
[Andrew:] here we go. It's. I'm. No, I don't. It'll. They're horrible things. hill only in first gear.
[Sanjay:] I think it's hard work innit? Going, more power, need a push behind, get up that bloody hill.
[Val:] Change gears.
[Sanjay:] , pay four, five, two hundred quid I think, cor bloody hell. Grass.
[Andrew:] That's what we were saying, well why does everybody buy to then?
[Val:] Exactly, latest craze.
[Sanjay:] Course it is, how do you buy, why do you buy a bike with no mudguards for? Said to Bert that got to be a right dopey dick to ride a bike with no mudguards on. [LAUGHTER] Wouldn't say he had to buy a pair, track bike, he's make their own up. He said I on the back at least.
[Val:] Mm.
[Sanjay:] Still there you are, glad somebody making some profit, just shows what we do buy, don't we? I tell you I couldn't get going at all not.
[Andrew:] [LAUGHTER] I could beat you.
[Val:] [LAUGHTER] He could. Andy.
[Andrew:] I thought, I thought there were gonna be a good ride, but.
[Val:] Like Andrew's.
[Andrew:] He probably got the rough one. [LAUGHTER]
[Val:] Like Andrew.
[Andrew:] Yeah, that was, that was similar sort of ride hard bloody work.
[Val:] Yeah.
[Andrew:] All right up round here ideal, up and down the bumps over the guard, but when you get it out on the road, very hard work, similar sort of ride, well I suppose it will be, run around the you've gotta push around...
[Sanjay:] Alright if you're double fit I suppose, and you've got a bit more help to around.
[Andrew:] Yes. I only took three quarters of an hour to get there. [sniff] It took about just over half an hour to get back. How's that for straight down Lane, straight over lights up hill, along the top here. Well it's still not bad at. cold last night,, far old long trot down from hill, innit? The Bells, it's all down hill until you hit all down hill. Yeah. nice and, nice, but even then they couldn't really. Well I want something in between, like the old sports, straight down the bike job.
[Sanjay:] Well is he gonna ride on one man's? Mind probably more comfortable than the base weren't they?
[Andrew:] I got used to them. I, yeah, I drove up, up there and back, like, my leg don't ache, they ached a bit at a time, but that, you know that bone you get, each side of your keep your thumb there, you've got that bone, underneath there's a bone there, you might, or the bottom bone that you'll sit on, you know when you sit still you get that bone.
[Sanjay:] Tail bone.
[Andrew:] No, the bottom here, you've got two, you've got two, just in there, in there you got the bones.
[Sanjay:] Pelvis.
[Andrew:] Might be the bottom of your pelvis, in there.
[Sanjay:] Yeah.
[Andrew:] Bloody hurt it bruises, you sit on it and it doesn't, I thought I might, I suppose after a while you'll get blisters but it's bruised, when you sit on the bloody thing.
[Sanjay:] And they sit
[Andrew:] To get a softer saddle you might get other problems. You might get other problems.
[Sanjay:] You get sore bones sitting down on anything.
[Andrew:] Oh can do, yeah, yeah, yeah.
[Sanjay:] Especially for me.
[Andrew:] Yeah, oh crikey, yeah.
[Sanjay:] They all ride back.
[Andrew:] I thought we're gonna so we came out of Paul's place, behind Belmont Parade, up past the ponds there and that's and I'm knackered, I'm going up river, had no you start at the bottom of Belmont Parade, up those ponds up to the traffic lights where you change buses, that's all up hill and it's slow, and you've just started and you're not warm and it's like running out of here, running up that hill there, now you could run up that hill if you got, if you had sort of round a couple of times round nice, no one so more ready to go, you'd run up there, you come out of here, run down here, not warm, feel you get, well I come out of there and, and you get, you go up past that set of traffic lights, you go up and you're still struggling past The Bull, that's still up hill, you get to the, just round that bend and it starts dropping down, and it's a gradual drop down, below the roundabout and the next roundabout's pretty level there, not too bad a roundabout, right the way across to Scades Hill, went down Scades Hill, right the way down to Alton, bottom of Alton high street, came out by the toilets at White Hart to High Street, up to house. Mhm.
[Sanjay:] That's a bit of a drag.
[Andrew:] Yeah.
[Sanjay:] That's a bit of a long drag that one, not that Paul take open up a bit there and go a bit faster, level, but that was a bit Well's done a left up to Chell's Field and that, bloody that killed him, I bet, you know the bit I mean, and up over the fields, where you go through the fields and fields, that was the killer, cos and coming back Bell's straight round to, got to the bottom, Hill wasn't too bad. It's a short, sharp, you can see it there, you get to the top of it, get up to your roundabout, we hang a right, and the next, it's a bit of a drag all the way up, you save coming, coming the other way it's down hill, from just past The Bull, until you get to the, almost to that junction you turn off the top and you're going up hill, just slowly, but cor, you get up to that, our junction, she drops down, we went straight down through the High Street, and we hung a right in the one way system, turn left, didn't get, quite get to Green Lane, turn left and up we come round the Green Lane, up and in the back way. Mm. I say, it took us three quarters of an hour to get there, three quarters of an hour to get there, just over the half an hour getting back. Mind you got short that was a killer up round by place. I reckon we got down from The Bells, Chell's Field, to the bottom of, six, seven minutes. Might be a bit more than that, but erm, could of been nine. She said wouldn't get up hill... How these blokes go I don't know, aren't they?
[Andrew:] Mm...
[Sanjay:] Mind you, it's the bloke in the front keeps don't he? Keep tucked in behind the side always said to you, the bloke in the front, mate, he does all the donkey work, picking up drags you round don't it? Whether he punches hole in the wind, in the air or not I dunno, like cards.
[Andrew:] Yeah.
[Sanjay:] He does seem eager, up behind some, long as you get a right distance, too far and you get oh, they're fighting it again, whereas you can get right up. We were thinking of the car, a slower car, could overtake a by getting up behind you, and when you coming out, as soon as he comes out
[Andrew:] Yeah.
[Sanjay:] he's got to go back again.
[Andrew:] That's what I thought.
[Sanjay:] But they don't, do they? You get, or you get two cars of equal speed, along straight
[Andrew:] Well it's a memento innit?
[Sanjay:] one get, yeah, one gets up behind it and can in the back I suppose, but they go after they, and then, you think as soon as you pull out, you're gonna get all that, yeah, he's gonna get all that, but they don't do they? They don't. Gotta be a reason for that I suppose. Cos they're going flat out when they're like that, it's not like you gonna say like, when you go on a, like overtake mode, when you're like that, they are flat out down the straight, all you go to get a out.
[Andrew:] Mm.
[Sanjay:] It's not like
[Andrew:] He goes
[Sanjay:] Yes, it's not like he's going, he's, he's going faster than this geezer, he's not, he's getting a drag from him, then all of a sudden he comes out and he goes faster you think, explain a little bit more on the old.
[Andrew:] I really don't know.
[Sanjay:] same lines, but, he know he, you assume that as soon as you got outside him, that bloody draft would come round and push him back and the other bloke would carry on.
[Andrew:] Yeah.
[Sanjay:] We might have a bit of a winner tonight.
[Andrew:] Mm, pretty quick aren't they?
[Sanjay:] They're first and second.
[Andrew:] Yep.
[Sanjay:] tend to blow up do they? Mansell tends to break him don't he?
[Andrew:] Yep.
[Sanjay:] The other bloke tends to run out of road a bit don't he?
[Andrew:] Aye we
[Sanjay:] Bit erratic innit?
[Andrew:] Yeah, he's not a real charger is he?
[Sanjay:] No. The only thing that I will do, that he might do, he might keep, cos once gets away mate that's he might keep him behind.
[Andrew:] Mm.
[Sanjay:] Yeah, not used to driving behind is he?
[Andrew:] No.
[Sanjay:] He's always had to keep that bloody thing.
[Andrew:] Yeah. Ferrari or something.
[Sanjay:] Yeah.
[Andrew:] How comes you only stayed at the Curry House?
[speaker005:] Ha, ha, no I never.
[Andrew:] Ha?
[speaker005:] No I'm actually.
[Andrew:] Fucking hell. Did you have money?
[John:] About a fiver.
[Andrew:] [LAUGHTER]
[speaker005:] money, so I ponce off him, you know, was well got a free curry a free beer. [radio on]
[Andrew:] I must say, is the heavy way.
[speaker005:] Yeah [LAUGHTER] where were we doing that?
[Andrew:] Way down to a.
[speaker005:] Yes, well that. Where do you lot got with last night, pissed off..
[Andrew:] It's not, it's people don't understand or something..
[speaker005:] Y M C A whatever.
[John:] [singing] Y M C A []. [radio]
[Andrew:] Makes me
[speaker005:] Oh fucking hell. goes erm, oh sort of.
[Andrew:] [singing] Best part of breaking up, you making up, best part of breaking up []
[speaker005:] Breaking up, you, best part of breaking up
[John:] Breaking up, you, news on waking up
[Andrew:] And you used to funky little reggae, oh my god [radio in background] singing.
[speaker005:] Singing
[John:] Singing
[Andrew:] They all, even all the girls that were screaming like yeah
[speaker005:] Yeah.
[John:] Yeah.
[Andrew:] Getting.
[speaker005:] They're bloody.
[Jon:] Right, anybody else? There should be a timetable at sometime.
[speaker005:] Yeah there is. Eh do. Already, Thursday.
[Jon:] It's what this Thursday?
[speaker005:] Next Thursday.
[Jon:] Alright. [LAUGHTER] If it's, if it's the first Thursday. Eh, right if you've got one of the the two plus three, have we, have we all got these, yeah? Yeah, have we got these? These complex questions. The one where... that one number eight and it's, it's got that complex number, that's the one we looked at just before the end of half term, yeah. Where you got number, so what you do is you multiply by the complex conjugate, top and bottom, if we do that, it comes out, out of multiple of one. I think it's a is it? Yeah it is.
[speaker005:] Oh.
[Jon:] Oh it is.
[speaker005:] Yeah, half.
[Jon:] It's a half, now if it's a half of that. And then the second says show that that complex numbered to the power of four where that complex number is that complex number, so all you do is that four, that and then you get minus a corner. Yes, so that's the answers. So the two answers are land and the answer is minus a quarter, I'll pin that one on the board.
[speaker005:] [LAUGHTER]
[Jon:] Right, the second one... now I'm gonna do, is the one that's equals three plus four, yeah, and you have gotta write down in the form P plus Q I so it's the real bit plus the imaginary bit, one over Z. One over Z is one over three plus four I's, I think we'll do that. How do we go to the the form, a number plus times it by the convex conjugate, is sub three minus four I, three minus four I, and what we get is three minus four I, over twenty five, eh, that sound reasonable to three twenty fifths, minus four twenty fifths high and that's Q, I, and one over Z square... or the second bit, several ways to do this, what you can do is work out what the square is first, so if I do a little aside Z square, it's three plus four I square, which is nine plus three forty five, twenty four I, plus sixteen I square, which is twenty four I, divide seven, who's that, so one over Z square is one over, minus seven plus twenty four I. Multiply by the complex you get again, and work the Z square that's pretty hard to multiply M, I, square minus one, do that by changing the imaginary, and multiply by, then you get an answer. You could square that, you could square that complex number, right, if that's, because one over Z is square one over Z, one over squared, Yeah, problems, cos. once you've got one over Z squared, if I work it out, you get minus seven, minus twenty four I over, ten sevens erm... oh, so you get forty nine on the bottom is that? No, no, not forty nine. That's not forty nine, it's erm, that's twenty four, which is seven, twenty four, twenty five, twenty six, six hundred and twenty five. What's that? So we get minus seven of six, two, five, minus twenty four I, over six, two, five. Right that's the, the complex number one over Z square, that's the answer. Right, you're, you're happy about how I got that?
[speaker005:] Yes. Yes. Yes.
[Jon:] a bit louder,, a just, seven square, minus seven, minus seven, gives me plus forty nine yeah?
[speaker005:] Yeah.
[Jon:] The minus, seven times that, we could be plus something, and an seven times that one would give you minus pass onto that, then twenty four times twenty four is five hundred and seventy six, I square, for it's minus I square, minus formula cos then when I add to add I get six hundred and twenty five, it's just, it's one, you know like the three, four, five, triangle, in Pythagoras, yeah, you know, when you get three, four, five, and you can make them three squared, four squared, so is five squared, right, well, seven, twenty four, twenty five, is another one of those, right that's how I knew seven, twenty four, I knew is six hundred and twenty five, that's how I, that's how I knew it's. Anyway we get these complex done, and you can check that, and that fits the, right, and then the second part of the question t is find the argument Well the argument, remember what the argument is? It's time by the minus one, which bit's on top? The imaginary bit's on top, so I've got twenty four over six, two, five, divide by seven to go over six, two, five. Eh, have you got fractions like that? Something over six hundred and twenty five, divided by something over six hundred and twenty five, now that is exactly the same as just a twenty four over seven, cos the six twenty five will cancel out. If I do twenty four divide by seven inverse time, I'll get an. Well, now, what's the anybody got a calculator with them? Twenty four divide by seven, inverse time, got a.
[speaker005:] Well what sort it out.
[Jon:] Twenty four, divide by seven, it's three point six,, I mean it's definitely of degrees.
[speaker005:] [cough]
[Jon:] , one point nine degrees. So we get the one point nine degrees, now, we've got to interpret that now. Now, you remember the really big puzzle on there, the imaginary bit goes there, and minus seven of something along the route bit and minus twenty four of them, so I'm going minus seven six hundred and twenty fifths there, minus twenty four, seven, so the actual lines go like that, so the one point nine at that angle, so the actual is going to be which is two sixty one point nine. Right then, let's, that's what we was doing. Now if, well, certainly there's a lot more complicated things in complex numbers, you should, all you really done, is to, this thing about the complex you get them work out some algebra, you go out and Z square some algebra and then you've done the complex with some algebra and with the use of plus and minus signs in there, it's a little bit tricky, but nothing, that, that, at A level that you shouldn't be able to handle, right, and once you've got that you look for some new, just, working and the least, and deciding what happened when you've actually got. That really, I mean that's six marks on the yellow paper, at that level that's really six per cent, but really it's all, that, that's, that, looking at that, that is one of the easier questions I would deal out, very easy. That's definitely one of the easier questions I would deal out. No,, all the complex numbers that you get on that, on that maths, are in similar, you should be able to do them, that is one of the key questions... If you think this is hard, wait until we go through, go through, representing back to equations.
[speaker005:] Yeah. No worries. Yeah.
[Jon:] You'll probably be able to that.
[speaker005:] [LAUGHTER] yeah probably. Is the, the difficult stuff?
[Jon:] Right next question is the one where you're given these two complex numbers, and you're asked to show the, the modules of Z one squared is two times the modules of Z two squared. So all it is, is, says, sure that that's that, so what I'm gonna do is say the modules of Z one is the square root of five squared plus one squared, so if I want the modules of Z one squared then all I've got is five squared plus one squared, cos when I've squared it, it gets rid of the square root, which is, don't you think,. No, so, Z two is the square root of two squared plus three squared... so I want Z two square, is two square plus three square, different in square root, so the two times is two times, well two square is four plus that,, that is that. Right next one, which is find the argument of Z one times Z two... Yeah, again a couple of different ways of doing it, what you can do is you find the argument of Z one, find the argument of Z two, and then what, what will we do for the answers, add them together to get the to, arguments to something worth together, we add them, or we can work out Z one times Z two and then just find a modulist of that complex number, now which way do you want to do it?
[speaker005:] First way. Go on, it's up to you. Go on. [LAUGHTER]
[Jon:] John said one.
[speaker005:] working out a modules you have to find the
[Jon:] Sorry did that one, I've got to accept it, right, find the, find find the, is up that way somewhere, that's fine, that's one, argument of that is, four over five inverse time. one divided by five, inverse time
[speaker005:] Three, eight, one, seven.
[Jon:] Seventy eh.
[speaker005:] forty five degrees.
[Jon:] One divided by five, have you ever put, one divided by five? Must be less than one five..
[speaker005:] Yeah, we're waiting for a.
[Jon:] Good, Z two is minus two plus three, minus two plus three I.
[speaker005:] [cough]
[Jon:] So that's two, that's three, so three, one forty five inverse time what'll we get? One point five inverse time, fifty six point three is in there, so the answer we want is minus two, one, three... one, two, three,, seven, so add that to and I hear one, two, four,.
[Andrew:] So that's R Z, one Z two, that's two R's together and then, what I calculate the side B, the square root of sixty minus thirty I, eh this about the hardest figure that I can do in complex numbers, the square root of sixteen, minus thirty I. Must n't, sixteen minus thirty I, but we want the square root of that, to begin plus D times. Oops then if I square both sides of that equation, then sixteen, minus thirty nine equals the A plus B, I, square, yeah, that's just the square on both sides, so sixteen minus thirty nine equals square this out under A squared, plus two give me, plus three squared, I squared. Yeah, that's just algebra, that's just what planners they've got. If I were back at the A squared, I squared is minus one, so I've got minus three squared, there's two give me by I... Equals minus thirty nine, now because those two complex numbers are the same [sneeze] are the same, so sixteen is E S squared minus three square, the imaginary grids are also the same, so minus thirty equals two, eight B. Don't really imaginary grid on this side, imaginary grid on that side, from which, if I second one, you can see A, that A equals minus fifteen over three. There take for two and what are the two categories turning to get fifteen over three. No, nothing, nothing fantastic, brilliant, yet, then substitute all that into the other one, so sixteen equals minus fifteen over B squared minus B squared, still nothing fantastic eh, sixteen equals five square when I get two, two, five, over three squared minus three squared. Yeah, that's just square. Square root has becomes, fifteen squared two plus five, B on the boxed squared, three square. Get rid of the, nobody has any questions? Multiply through sixteen B square equals two, two, five minus B to the four, cos B squared have B squared, multiply B square and I get that. Now bring it all over the left hand side and we'll get B to the plus sixteen B square, minus two, two, five equals what?... That's just bringing that minus B squared,, bring that to twenty five minus.
[speaker005:] . We came to find out. Yeah.
[Jon:] Like, you got, I mean put the other side of the. Cos what we're going to do now, is real... what, really what this is, this is like a quadratic equation, it is B square, squared plus sixty B squared, minus two, two, five,, so that's a quadratic equation, but instead of saying X square, I'm saying B square, square, plus sixteen B square. So what I'm gonna do is use the, let's see, it's minus three, plus I'll minus the square in B square, sixteen strand, minus four times the eight, nine C, well I'm gonna do that, four times eight, nine C, equals plus nine all over to A, just two.
[speaker005:] Can't you do the main this way?
[Jon:] You can't evaporate it, yeah. It vaporises fairly easy.
[speaker005:] Well I got.
[Jon:] Very, very easily vaporises it, but and then when I do that I get minus sixteen plus I minus the square root off one thousand, one hundred and fifty six, all over two, plus minus sixteen, plus or minus what's the square root of one thousand one hundred and fifty six?
[speaker005:] Thirty six is it?
[Jon:] I don't know. Thirty four oh, thirty four all over two. All over two, then if you pass, spread them over minus sixteen add thirty four gives me eighteen over two, or if I do minus thirty four I get nine over two, that'll be plus nine or even minus twenty five...
[speaker005:] Eh, start off with, cos you've gone all the way through that.
[Jon:] Yeah, eh with the end you could have B equals minus fifteen over here and you would have still got the same answer. Now we've got this far, so, now remember what we're doing, we're finding out what B squared is, so either, B squared is nine or B squared is minus twenty five. Yeah, now then, one of the things, when we get this complex numbers and B, itself is a real number and B itself is a real number, right, plus B, I, is actually what we call a complex number, if those two apart, they're just numbers. So we can't have B square in twenty five, twenty five cos nothing exists, there twenty five., well we have got complex numbers, but we can't have B itself in the complex number, right, so B square must be nine, so either... B is plus three or B is minus three, one or the two...
[speaker005:] [cough]
[Jon:] Now if B is plus three, then going back to me formula here is going to be minus five, cos if I put the three in it there, I get minus five from there. And if B is minus three, then here is plus three, plus five., so the complex number that is the square root, is either two in that pair, minus five, plus three, nine, or it is five minus three, nine, so it's either that one, or it's that one, and we can write that down very, very simply because that one and that one are just the opposite sides, but either plus or minus.
[speaker005:] I suppose.
[Jon:] Three, five, and when you've worked these square roots out, they always come out the opposites sides, it's always plus or minus,, always, always, always. When you work these square root things out, whatever square root is, it's always one, like one plus three, minus five, the other one's minus three plus five, they're always like that. Cos they're what we call complex conjugals.
[speaker005:] Do we gets points then sir, if the other one was twenty five?
[Jon:] Yeah, it's just pure coincidence, it's just the way that trotting around, I think what we're trying to do was to say, something wrong in exam book, plus, plus, which is not liked, but, I don't think they are the alike. Cos they don't actually, if you do something like that, say you put plus five, minus five and then sit down and, you're the one that plus three and minus three you don't actually lose marks doing something wrong, you cannot be penalised for doing it wrong, you can only gain credit for doing something right, because they'll, give you five marks to doing that bit right and then knock three off for doing something else wrong, they, they would never give you penalty marks, they will only credit for doing things right, but so often it's quite like down as you want, you can't. All that's doing is, is the account against this sort of idea that you can always do it.
[speaker005:] Yeah.
[Jon:] Or like people come to you getting forty per cent and forty per cent was, of these,, then, the, he was was not as good as that one, but that one gets the B, that one gets the C, so you wanna. That's an interesting point that, any square root, any square root you always get two answers for square roots yeah, it's always plus thing and minus thing, in complex numbers, when you get complex numbers there are always what we call complex conjugators, if you drew them on them, on them diagram, right, if you drew them on the diagram, what'll you get, plus five minus three I, plus five, minus three I, and then... and then we get minus five, plus three I,... You get plus and minus there.
[speaker005:] Pardon?
[Jon:] That's, but that is the hardest thing, now the hard thing about that is not actual complex numbers, it's sort of these equations which is something else you've done, equations, but the other one, haven't really got time, the other one complex numbers said what it said to given by that, you've got to draw them two on a diagram, that, very very slow, calculate the modules as Z more minus Z two, what work is what Z one minus two is, they work in modules. Work out what Z one divided by Z two is, and then find the argument of it and give your answer in ratings, there. [alarm ringing] The last little bit it says, give your answer in ratings, suppose W, right I just, suppose W had the seven plus fifteen I, how you gonna get R, W in ratings? Well one way you can do it, is press the ratings button on your calculator, press fifteen divide by seven and then press the ratings button, so, just do that, change it on the ratings... one, yeah, press fifteen divide by seven, in.
[speaker005:] One point one, three, four.
[Jon:] One point one, three, four, right, one point one, three, four, right, OK do it like that, although that doesn't mean anything at all here, that's the right answer, because you, you've in ratings, right, if you wanted to, put it back on degrees, ah now press fifteen divide by seven equals and then press inverse.
[speaker005:] Sixty four point nine.
[Jon:] Sixty four point nine, well sixty five point nought degrees, so sixty five degrees technically, right, that number is sixty five degrees, now, one pi is one hundred and eighty, pi is the same as one hundred and eighty degrees, so if we've got sixty five degrees what we've got is sixty five over a hundred and eighty, pi.
[speaker005:] Sorry?
[Jon:] Do that, do that on sixty five divide by one hundred and eighty, multiply by the pi on your calculator, just one second Robin, yeah, it's usually, it's just theatrical, you should get, yeah, so you get the same answer, so you can either work it on ratings or you can write it like that, you could've actually left it like that, if you come to the third by, you put thirteen over what is it? eh
[speaker005:] Multiple fifteen.