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. :)

$e^{i\theta} = (\cos\theta+i\sin\theta),e^{i\alpha} = (\cos\alpha+i\sin\alpha)$
$e^{i\theta}e^{i\alpha} = (\cos\theta+i\sin\theta)(\cos\alpha+i\sin\alpha)\\
=\cos\theta cos\alpha - \sin\theta\sin\alpha +i(\sin\theta cos\alpha + \cos\theta\sin\alpha) = \cos(\theta+\alpha) +i\sin(\theta+\alpha) = e^{i{(\theta+\alpha)}}$
