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Let $z = i^{{}^{64}C_{0}} + i^{{}^{64}C_{1}} + i^{{}^{64}C_{2}} + ... + i^{{}^{64}C_{64}},$ where $i = \sqrt{- 1}$ , be a complex number. Then which of the following is correct ?

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$Re [{(z - 63)}^{2022}] > 0$

$Im [{(z - 60)}^{2022}] = 0$

$Im [{(z - 59)}^{2022}] > 0$

$Re [{(z - 61)}^{2022}] < 0$

answer is C.

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Detailed Solution

$z = 61 + 2 i$

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