Complex Variable help

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November 13th 2012, 06:43 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 $|e^{5z+3i+2} + e^{iz^2}|$ $\not\leq$ $e^{5x + 2} + e^{-2xy}$
November 13th 2012, 06:53 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?
November 13th 2012, 07:34 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?