# The exponential identity

1. Jan 30, 2010

### rbwang1225

1. The problem statement, all variables and given/known data
Let z=x+iy prove that Exp[z1]*Exp[z2]=Exp[z1+z2]

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

3. The attempt at a solution

2. Jan 31, 2010

### 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).

3. Feb 1, 2010

### rbwang1225

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