# Prove that

1. Jan 28, 2009

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

if z = 1/sqrt 2 + i/sqrt2

2. Relevant equations

show that z + z4n+1 = 0,
when n is any odd integer.

if n is an even integer, find z + z4n+1 in rectangular form.

3. The attempt at a solution

I have no clue where to start...

2. Jan 28, 2009

### ravioli

What's z in polar form? Also note that $$\text{z} + \text{z} ^ \text{4n+1} = \text{z} * ( 1 + \text{z} ^ \text{4n} )=0$$