# complex variable

• Feb 10th 2011, 10:27 AM
eleahy
complex variable
im struggling with what seems to be an easy question
it asks to find [COLOR=rgb(0, 0, 0)]all solutions to the following equations
- (e^2z)-2i=0
-(z-i)^5=1
are two im sure there not hard because he has given us ten to do but just don't see how to do them or is it as simple as jsut breaking them down and putting z=x+iy
[/COLOR]
• Feb 10th 2011, 10:31 AM
Plato
Just to be clear, is the first problem $e^{2z}-2i=0~?$
• Feb 10th 2011, 10:45 AM
eleahy
ya think if i could figure out one id be able to go with the rest of them :)
• Feb 10th 2011, 10:48 AM
Plato
That is the same as $e^{2z}=2i$ so $2z=\log(2i)$.
Do you understand the complex logarithm?
• Feb 10th 2011, 10:52 AM
eleahy
not really ill look it up
• Feb 10th 2011, 10:56 AM
eleahy
in these questions am i just looking for values of z yes??
• Feb 10th 2011, 11:01 AM
eleahy
if its sin(z)+2i=0 any idea how id get rid of the sin? sorry last question this stuff is hard!!
• Feb 10th 2011, 11:41 AM
Plato
$\sin(z)=\sin(x)\cosh(y)+i~\cos(x)\sinh(y)$