Question

If \( \omega \) is a complex cube root of unity, then \[ \cos\left(\left(\omega^{1234} + \omega^{2021}\right)\pi - \frac{\pi}{4}\right) = \]

• A. \(-\frac{1}{\sqrt{2}}\)
• B. \(\frac{1}{\sqrt{2}}\)
• C. \(\frac{\sqrt{3}}{2}\)
• D. \(-\frac{\sqrt{3}}{2}\)

Hint:

For cube roots of unity: \(\omega^3 = 1\), \(1+\omega+\omega^2=0\), so \(\omega+\omega^2=-1\). Reduce exponents mod 3.

Answer 1

The Correct Option is A