Q:

Solving for the missing real and imaginary parts that satisfy the following equation

I'm trying to solve for the real and imaginary parts of the equation:
$(3+xi)(y+3i)=-6+17i$ Can I just isolate each individual part and set it equal to its respective part?
Thanks in advance

A:

Yes.
If $z = a + bi$ and $w = c + di$ are complex numbers then $z = w$ if and only if $a = c$ and $b = d$. That is, if and only if their real and imaginary parts coincide.

