# Math Help - complex numbers

1. ## complex numbers

if z = x+yi prove that:

abs(e^z)=e^x

so I can show that e^z = e^x * cisy, I'm not sure what how the absolute value will change this.

2. Two big hints.
$\left| {cis(t)} \right| = \left| {\cos (t) + i\sin (t)} \right| = \sqrt {\cos ^2 (t) + \sin ^2 (t)} = ?$
$\left| {zw} \right| = \left| z \right|\left| w \right|$

3. $e^{z} = e^{x}(\cos y + i \sin y)$. Thus $|e^{z}| = |e^{x}| \cdot |\cos y + i \sin y| = e^{x}$. As Plato hinted, the modulus of the second term is $1$.