Complex Numbers Proof

[TheWrathOfMath]

Given that z and w are complex numbers whose sum is not zero, prove that [z^(1996)-w^(1996)] / (z+w) is a pure imaginary number.

 

[Deleted member 4993]

Given that z and w are complex numbers whose sum is not zero, prove that [z^(1996)-w^(1996)] / z+w is a pure imaginary number.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[TheWrathOfMath]

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

My teacher taught us the whole topic of complex numbers in only three hours, so I barely had the chance to practice.
I do not know where to start, frankly.