# Thread: Help with proving Complex variable equations

1. ## 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

2. ## Re: Help with proving Complex variable equations

Originally Posted by flametag2
(a) If $e^z$ E R. show that Im $z = n \pi$. where n E Z
$$e^{z}=e^{x}(\cos(y)+i\sin(y)$$ gives $e^{z}=e^{x}(\cos(y)+i\sin(y))$.
You can see that is real only if $y=n\pi$ where $n\in\mathbb{Z}$.