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If z-1/z=I. Then find z ^2015-1/z2015

If z-1/z=I. Then find z^2015-1/z2015

Grade:12

1 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
6 years ago
z-1/z is actually z – z(bar) which is equal to 2isin (theta)
Solving this equation you will get sin (theta) = ½ or theta = 30
Now z^2015-1/z2015 is again 2isin2015(theta). 2015*30/360 gives 330.
So the answer is 2isin(-30) i.e. -i

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