Help with proving Complex variable equations

Hello, Could someone please Help with proving the Complex variable equation

(a) If $\displaystyle e^z$ E R. show that Im $\displaystyle z = n \pi$. where n E Z

and if [TEX]e^z E i . R. then what is z =?

Also, if someone knows of any book online or a resource that would help me with Basic Trancendental Functions chapter in complex variables, it will be GREATLY appreciated. The book that we have is completely useless

Re: Help with proving Complex variable equations

Quote:

Originally Posted by

**flametag2** Hello, Could someone please Help with proving the Complex variable equation

(a) If $\displaystyle e^z$ E R. show that Im $\displaystyle z = n \pi$. where n E Z

and if [TEX]e^z E i . R[COLOR=#444444][FONT=verdana]. then what is z =?

You can use LaTeX code to make it more readable.

[tex]e^{z}=e^{x}(\cos(y)+i\sin(y)[/tex] gives $\displaystyle e^{z}=e^{x}(\cos(y)+i\sin(y))$.

You can see that is real only if $\displaystyle y=n\pi$ where $\displaystyle n\in\mathbb{Z}$.

I cannot read the second part of the question.