(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello, I am supposed to express the and the phase part of expression:

[itex]\displaystyle{S=\frac{k}{\sqrt{1+i\gamma_0}} \cdot exp\left(\frac{z}{1 + i\gamma_0}\right)}[/itex]

2. Relevant equations

The answer should be in the form:

[itex]\displaystyle{S=a(\gamma_0) \cdot exp\left(i\varphi(\gamma_0)\right)}[/itex]

3. The attempt at a solution

Well, its clear(probably) that for the amplitude part I just have to multiply this equation by its complex conjugate and take a square root out of the result. This leaves me with the expression of:

[itex]\displaystyle{ a(\gamma_0)=\frac{k}{\left(1+\gamma^2_0\right)^{1/4}} \cdot exp\left(\frac{z}{1+\gamma^2_0}\right) }[/itex]

However, I dont quite understand how to get the complex(phase) part of the number? A hint where to start would be very gladly accepted :), thank you.

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# Separating real and complex parts of a number

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