Help with proving Complex variable equations

• November 13th 2012, 06:54 AM
flametag2
Help with proving Complex variable equations

(a) If $e^z$ E R. show that Im $z = n \pi$. 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
• November 13th 2012, 08:21 AM
Plato
Re: Help with proving Complex variable equations
Quote:

Originally Posted by flametag2

(a) If $e^z$ E R. show that Im $z = n \pi$. 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.
$$e^{z}=e^{x}(\cos(y)+i\sin(y)$$ gives $e^{z}=e^{x}(\cos(y)+i\sin(y))$.

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

I cannot read the second part of the question.