Question:
If \( \omega = \frac{-1 + \sqrt{3}i}{2} \), then \( (3 + \omega + 3\omega^2) \) is:
If \( \omega = \frac{-1 + \sqrt{3}i}{2} \), then \( (3 + \omega + 3\omega^2) \) is:
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The cube roots of unity, \( \omega \) and \( \omega^2 \), satisfy the equation \( \omega^3 = 1 \) and can simplify many complex expressions.
Updated On: Jan 12, 2026
- 16
- -16
- 16\( \omega \)
- 16\( \omega^2 \)
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The Correct Option is B
Solution and Explanation
Using the value of \( \omega \), which is a cube root of unity, we substitute and simplify the expression to get the result as -16.
Final Answer: \[ \boxed{-16} \]
Final Answer: \[ \boxed{-16} \]
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