Product of complex exponential

Question

I'm having trouble resolving this issue on complex numbers involvendo principle of induction.

As I show that:

$$e^{i\theta_1} e^{i\theta_2}\cdots e^{i\theta_n}=e^{i(\theta_1+\theta_2+\cdots+\theta_n)}$$

Answer 1

you can use summation formula of sinx & cosx. That is, De Moivre's formula.

http://en.wikipedia.org/wiki/De_Moivre%27s_formula