Proving Properties of z When n is Odd/Even Integer

[maobadi]

Homework Statement

if z = 1/sqrt 2 + i/sqrt2

Homework 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.

The Attempt at a Solution

I have no clue where to start...

 

[ravioli]

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