# Proof of complex number identity

1. Jul 15, 2010

### Gameowner

1. The problem statement, all variables and given/known data

Attached question

2. Relevant equations

3. The attempt at a solution

The second part of question is relatively easy, it is the first part of the question where I need help with(using arg zw = arg z + arg w to show arg z^n = n arg z).

Also, is the question asking to proof de Moivre's formula with the identity arg zw = arg z + arg w? or just proof LHS=RHS?

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2. Jul 15, 2010

### alxm

I guess it's the induction that's causing problems. Show that it's true for z2. Then show that if it's true for zn, that it's also true for zn+1.

The second part uses the relation you proved in the first part.

3. Jul 16, 2010

### eumyang

The base case would be for z1, I thought. In any event, it's easy to prove.
The inductive case: assume true for n = k, show that it's true for n = k + 1.
Here's a hint: xa + 1= (xa)(x).

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