SOLUTION: When z = (1+i)/(1-i), prove that z+z²+z³+z⁴=0

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Question 987127: When z = (1+i)/(1-i), prove that z+z²+z³+z⁴=0
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
z=%281%2Bi%29%2F%281-i%29

z%22%22=%22%22%281%2Bi%29%2F%281-i%29%22%D7%22%281%2Bi%29%2F%281%2Bi%29%22%22=%22%22%281%2B2i%2Bi%5E2%29%2F%281-i%5E2%29%22%22=%22%22%281%2B2i%2B%28-1%29%29%2F%281-%28-1%29%29%22%22=%22%222i%2F2%22%22=%22%22i

z+z²+z³+z⁴ = i+i²+i³+i⁴ = i+(-1)+(i²×i)+(i²×i²) = i-1+(-1×i)+(-1×-1) =

i-1-i+1 = 0

Edwin