Proving the Exponential Identity for Complex Numbers

[rbwang1225]

Homework Statement

Let z=x+iy prove that Exp[z1]*Exp[z2]=Exp[z1+z2]

Homework Equations

Binomial thm (x+y)^n=Sum[Bin[n,k]*x^n-k*y^k,{k,1,n}]

The Attempt at a Solution

I have no idea about this question...

Please give me some help.

 

[HallsofIvy]

I don't see how the binomial theorem has anything to do with this. I think better would be
$$e^{a+ bi}= e^a(cos(b)+ i sin(b))$$
together with $e^{x+y}= e^x e^y$, cos(x+y)= cos(x)cos(y)- sin(x)sin(y), and sin(x+y)= sin(x)cos(y)+ cos(x)sin(y).

 

[rbwang1225]

The hint was given by my teacher, but I think he is a little unreliable.