Proving Properties of z When n is Odd/Even Integer

AI Thread Summary
To prove that z + z^(4n+1) = 0 for any odd integer n, it is essential to express z in polar form. The discussion highlights the need to manipulate the equation to show that z multiplied by (1 + z^(4n)) equals zero. For even integers, the goal is to find z + z^(4n+1) in rectangular form. The initial confusion indicates a lack of clarity on how to convert z to polar coordinates. Understanding these conversions is crucial for solving the problem effectively.
maobadi
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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...
 
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What's z in polar form? Also note that \text{z} + \text{z} ^ \text{4n+1} = \text{z} * ( 1 + \text{z} ^ \text{4n} )=0
 

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