Using Euler's Formula to prove $e^{i\theta}e^{i\alpha}=e^{i(\theta+ \alpha)}$ I have a homework question thats been puzzling me. It says:

Using Euler's Formula, prove the product property of the complex exponential: 
  $$e^{i\theta}e^{i\alpha}=e^{i(\theta+ \alpha)}$$

Besides knowing Euler's formula, I have no idea where to start so any help is appreciated. :)

Fix $y$ and let $f(x) = e^{ix} e^{iy}- e^{i(x+y)}$.
Note that $f(0)=0$ and
$f'(x) = (\sin x - i \cos x) (\cos y + i \sin y) - \sin (x+y) +i \cos (x+y) = 0$.
Hence $f(x) = 0$ for all $x$.
