# Complex Variable help

• Nov 13th 2012, 07:43 AM
flametag2
Complex Variable help
Could someone help me and explain how to write teh following in terms of x and y. I have seen some examples but I dont seem to be able to do this one on my own.

$|e^{5z+3i+2}|$ and $|e^{iz^2}|$

and show that $|e^{5z+3i+2} + e^{iz^2}|$ $\not\leq$ $e^{5x + 2} + e^{-2xy}$
• Nov 13th 2012, 07:53 AM
HallsofIvy
Re: Complex Variable help
Quote:

Originally Posted by flametag2
Could someone help me and explain how to write teh following in terms of x and y. I have seen some examples but I dont seem to be able to do this one on my own.

$|e^{5z+3i+2}|$ and $|e^{iz^2}|$

What are you supposed to do with these? You should know that $|e^{ia}|$ is equal to 1 for any a.
Amd $|e^{5z+ 3i+ 2}|= |e^{5z}||e^{3i}||e^2|$. And, again, $|e^{3i}|= 1$.

Quote:

and show that $|e^{5z+3i+2} + e^{iz^2}|$ $\not\leq$ $e^{5x + 2} + e^{-2xy}$
Are we to assume here that z= x+ iy?
• Nov 13th 2012, 08:34 AM
Plato
Re: Complex Variable help
Quote:

Originally Posted by flametag2
Could someone help me and explain how to write teh following in terms of x and y. I have seen some examples but I dont seem to be able to do this one on my own.
$|e^{5z+3i+2}|$ and $|e^{iz^2}|$
and show that $|e^{5z+3i+2} + e^{iz^2}|$ $\not\leq$ $e^{5x + 2} + e^{-2xy}$

Where did you find this question?

It is easy to show that $\left|e^z\right|=e^{\text{Re}(z)}$.

Because $|z+w|\le |z|+|w|$ for all complex $z~\&~w$, how can the inequality not hold?