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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.

Andrés E. Caicedo
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Shivji
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2 Answers2

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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.

Lion
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  • OP has changed the variables in his post (and it makes sense this now). – M. Vinay Jun 14 '14 at 03:53
  • That I know but how do I seperate it in real and imaginary part when the complex number is inside a log funciton?. In the above equation forget the LHS. I need to solve the RHS $\log(x+jy)$ and seperate this into the form a + jb – Shivji Jun 14 '14 at 03:53
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You could convert the complex number from algebraic to polar form $r\cdot e^{j\theta} $ where $r=\sqrt{x^2+y^2} $ and $\theta=\arctan\left(\frac{y}{x}\right) $

After that, you can split the $\log$ function into real and imaginary parts:

$$ \log(r\cdot e^{j\theta}) =\log(r) +j\theta\log(e) $$ $$ = \log(r) +j\theta $$ (assuming natural logarithm)

Tymric
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