Help with proving Complex variable equations

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

(a) If E R. show that Im . 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

E R

. show that Im . 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 .

You can see that is real only if where .

I cannot read the second part of the question.