Multiplying two imaginary numbers is a lot like multiplying a positive number with a negative number. If we say "go east by 2 × -3 miles", it means "rotate all of the way around (so that you are now facing west) and go 2×3 = 6 miles". Imaginary numbers work the same, except that you can rotate part way. If we say go "east by 2×3i miles", it means the same as if we had said "rotate until you are facing north, and then go 2×3 = 6 miles"
m ʌ l t ɪ p l aɪ ɪ ŋ WORD_BOUNDARY t uː WORD_BOUNDARY ɪ m æ d̠ʒ ɪ n ɛ ɹ i WORD_BOUNDARY n ʌ m b ə ɹ z WORD_BOUNDARY ɪ z WORD_BOUNDARY ʌ WORD_BOUNDARY l ɑ t WORD_BOUNDARY l aɪ k WORD_BOUNDARY m ʌ l t ɪ p l aɪ ɪ ŋ WORD_BOUNDARY ʌ WORD_BOUNDARY p ɑ z ɪ t ɪ v WORD_BOUNDARY n ʌ m b ə ɹ WORD_BOUNDARY w ɪ ð WORD_BOUNDARY ʌ WORD_BOUNDARY n ɛ ɡ ə t ɪ v WORD_BOUNDARY n ʌ m b ə ɹ WORD_BOUNDARY ɪ f WORD_BOUNDARY w iː WORD_BOUNDARY s eɪ WORD_BOUNDARY ɡ oʊ WORD_BOUNDARY iː s t WORD_BOUNDARY b aɪ WORD_BOUNDARY t uː WORD_BOUNDARY t aɪ m z WORD_BOUNDARY θ ɹ iː WORD_BOUNDARY m aɪ l z WORD_BOUNDARY ɪ t WORD_BOUNDARY m iː n z WORD_BOUNDARY ɹ oʊ t eɪ t WORD_BOUNDARY ɔ l WORD_BOUNDARY ʌ v ð ə WORD_BOUNDARY w eɪ WORD_BOUNDARY ə ɹ ɹ aʊ n d WORD_BOUNDARY s oʊ WORD_BOUNDARY ð æ t WORD_BOUNDARY j uː WORD_BOUNDARY ɑ ɹ WORD_BOUNDARY n aʊ WORD_BOUNDARY f eɪ s ɪ ŋ WORD_BOUNDARY w ɛ s t WORD_BOUNDARY æ n d WORD_BOUNDARY ɡ oʊ WORD_BOUNDARY t uː WORD_BOUNDARY t aɪ m z WORD_BOUNDARY θ ɹ iː WORD_BOUNDARY iː k w ə l z WORD_BOUNDARY s ɪ k s WORD_BOUNDARY m aɪ l z WORD_BOUNDARY ɪ m æ d̠ʒ ɪ n ɛ ɹ i WORD_BOUNDARY n ʌ m b ə ɹ z WORD_BOUNDARY w ɜː k WORD_BOUNDARY ð ə WORD_BOUNDARY s eɪ m WORD_BOUNDARY ɛ k s ɛ p t WORD_BOUNDARY ð æ t WORD_BOUNDARY j uː WORD_BOUNDARY k æ n WORD_BOUNDARY ɹ oʊ t eɪ t WORD_BOUNDARY p ɑ ɹ t WORD_BOUNDARY w eɪ WORD_BOUNDARY ɪ f WORD_BOUNDARY w iː WORD_BOUNDARY s eɪ WORD_BOUNDARY ɡ oʊ WORD_BOUNDARY iː s t WORD_BOUNDARY b aɪ WORD_BOUNDARY t uː WORD_BOUNDARY t aɪ m z WORD_BOUNDARY θ ɹ iː WORD_BOUNDARY aɪ WORD_BOUNDARY m aɪ l z WORD_BOUNDARY ɪ t WORD_BOUNDARY m iː n z WORD_BOUNDARY ð ə WORD_BOUNDARY s eɪ m WORD_BOUNDARY æ z WORD_BOUNDARY ɪ f WORD_BOUNDARY w iː WORD_BOUNDARY h æ d WORD_BOUNDARY s ɛ d WORD_BOUNDARY ɹ oʊ t eɪ t WORD_BOUNDARY ʌ n t ɪ l WORD_BOUNDARY j uː WORD_BOUNDARY ɑ ɹ WORD_BOUNDARY f eɪ s ɪ ŋ WORD_BOUNDARY n ɔ ɹ θ WORD_BOUNDARY æ n d WORD_BOUNDARY ð ɛ n WORD_BOUNDARY ɡ oʊ WORD_BOUNDARY t uː WORD_BOUNDARY t aɪ m z WORD_BOUNDARY θ ɹ iː WORD_BOUNDARY iː k w ə l z WORD_BOUNDARY s ɪ k s WORD_BOUNDARY m aɪ l z WORD_BOUNDARY