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Q.

If $ω$ is a complex cube root of unity, then $\cos [(ω^{1234} + ω^{2021}) π - \frac{π}{4}]$ is equal to

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a

$\frac{1}{\sqrt{2}}$

b

$\frac{- 1}{\sqrt{2}}$

c

$\frac{1}{2}$

d

$\frac{\sqrt{3}}{2}$

answer is D.

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Detailed Solution

$\cos [(ω^{1234} + ω^{2021}) π - \frac{π}{4}] = \cos [(ω + ω^{2}) π - \frac{π}{4}]$
$= - \frac{1}{\sqrt{2}}$

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