1. ## 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.

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

and show that $\displaystyle |e^{5z+3i+2} + e^{iz^2}|$ $\displaystyle \not\leq$ $\displaystyle e^{5x + 2} + e^{-2xy}$

2. ## Re: Complex Variable help

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.

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

and show that $\displaystyle |e^{5z+3i+2} + e^{iz^2}|$ $\displaystyle \not\leq$ $\displaystyle e^{5x + 2} + e^{-2xy}$
Are we to assume here that z= x+ iy?

3. ## Re: Complex Variable help

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.
$\displaystyle |e^{5z+3i+2}|$ and $\displaystyle |e^{iz^2}|$
and show that $\displaystyle |e^{5z+3i+2} + e^{iz^2}|$ $\displaystyle \not\leq$ $\displaystyle e^{5x + 2} + e^{-2xy}$
Where did you find this question?

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

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