$\displaystyle (e^z-1)(e^z-i)=0$

Can $\displaystyle e^z$ be isolated in any way?

I need to find all the solutions for $\displaystyle e^z$

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- Nov 28th 2011, 07:04 AMMathIsOhSoHardCan this be writen any differently?
$\displaystyle (e^z-1)(e^z-i)=0$

Can $\displaystyle e^z$ be isolated in any way?

I need to find all the solutions for $\displaystyle e^z$ - Nov 28th 2011, 07:07 AMSironRe: Can this be writen any differently?
Do you mean you want something of the form $\displaystyle e^z=...$? Yes, you're dealing with an equation of the form $\displaystyle a\cdot b=0$ which implies that $\displaystyle a=0 \ \mbox{or} \ b=0$ are the solutions.

- Nov 28th 2011, 07:08 AMMathIsOhSoHardRe: Can this be writen any differently?
I need to find the solutions for $\displaystyle e^z$.

I know how to find the solutions when it's written as $\displaystyle e^z=...$ but I have a hard time figuring this one out. - Nov 28th 2011, 07:11 AMSironRe: Can this be writen any differently?
- Nov 28th 2011, 07:14 AMMathIsOhSoHardRe: Can this be writen any differently?
- Nov 28th 2011, 07:20 AMMathIsOhSoHardRe: Can this be writen any differently?
If I solve for $\displaystyle e^z=1$ then I get the solution:

$\displaystyle z=2p \pi i$

If I solve for $\displaystyle e^z=i$ then I get the solution:

$\displaystyle z=i(\pi /2 + 2p \pi)$ - Nov 28th 2011, 07:22 AMPlatoRe: Can this be writen any differently?
- Nov 28th 2011, 07:27 AMMathIsOhSoHardRe: Can this be writen any differently?
- Nov 28th 2011, 07:38 AMPlatoRe: Can this be writen any differently?
- Nov 28th 2011, 07:42 AMMathIsOhSoHardRe: Can this be writen any differently?
This is taken straight out of my text book word by word (it is scanned):

http://img20.imageshack.us/img20/1263/solutionsn.jpg

Is it incorrect? - Nov 28th 2011, 07:48 AMPlatoRe: Can this be writen any differently?
- Nov 28th 2011, 07:58 AMMathIsOhSoHardRe: Can this be writen any differently?
- Nov 28th 2011, 08:05 AMPlatoRe: Can this be writen any differently?
That is correct.