1. Proof of Sine Addition Formula with complex numbers

Hi there,

I am stuck on a proof using complex numbers. I have tried almost everything but I seem to get nowhere. Here is the question .

Let a,b be complex numbers. Prove that sin(a+b)= sinacosb + sinbcosa

2. This is just a tedious problem.
Use $\sin (z) = \dfrac{{e^{iz} - e^{ - iz} }}
{{2i}}\;\& \,\cos (z) = \dfrac{{e^{iz} + e^{ - iz} }}
{2}$