COMEDK · Maths · 3. Complex Number
If \(\omega=\frac{-1+\sqrt{3 i}}{2} \operatorname{then}\left(3+\omega+3 \omega^{2}\right)^{4}\) is
- A \(16\)
- B \(-16\)
- C \(16 \omega\)
- D \(16 \omega^{2}\)
Answer & Solution
Correct Answer
(C) \(16 \omega\)
Step-by-step Solution
Detailed explanation
We have, \(\left(3+\omega+3 \omega^{2}\right)^{4}\) \(=\left(3+3 \omega+3 \omega^{2}-2 \omega\right)^{4}\) \(=\left[3\left(1+\omega+\omega^{2}\right)-2 \omega\right]^{4}\) \(=(3 \times 0-2 \omega)^{4}\) \(\left[\because 1+\omega+\omega^{2}=0\right.\) or…
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