If z = 3 2 + i 2 , i = - 1 then ( z 201 - i ) 8 is equal to [2026]

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Solution

Q.
If $z = \frac{\sqrt{3}}{2} + \frac{i}{2}, i = \sqrt{- 1}$ then ${(z^{201} - i)}^{8}$ is equal to [2026]

1 0

2 1

3 256

4 -1

Ans.
(3)

$z = \cos \frac{π}{6} + i \sin \frac{π}{6}$

$z^{201} = \cos (201 \frac{π}{6}) + i \sin (201 \frac{π}{6}) = - i$

${(z^{201} - i)}^{8} = {(- 2 i)}^{8} = 256$

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