JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

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Application +4 | -1

\omega

is a complex cube root of unity, then

\sin \left\{ {\left( {{\omega ^{10}} + {\omega ^{23}}\pi - \frac{\pi }{4}} \right)} \right\}

is equal to

View answer and explanation

Correct option: A

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

Option A (

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

) is correct because simplifying the expression inside the sine function using properties of complex cube roots of unity leads to

\sin(-\pi - \frac{\pi}{4}) = \frac{1}{\sqrt{2}}

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