[Math] How to separate out real and imaginary terms

Question

I have an equation like this:
$$a+ib = \log(x+iy).$$

I need to separate the real and imaginary part in RHS so that I can equate the real part of LHS to real part of RHS and imaginary to imaginary part of RHS.

Answer 1

Note your equation is equivalent to

$$ e^{a+jb}=a+jb\\ e^ae^{jb}=a+jb\\ e^a(\cos(b)+j\sin(b))=a+jb $$ Then real and imaginary parts have been separated.