Question

If \( \omega = \frac{-1 + \sqrt{3}i}{2} \), then \( (3 + \omega + 3\omega^2) \) is:

• A. 16
• B. -16
• C. 16\( \omega \)
• D. 16\( \omega^2 \)

Hint:

The cube roots of unity, \( \omega \) and \( \omega^2 \), satisfy the equation \( \omega^3 = 1 \) and can simplify many complex expressions.

Answer 1

The Correct Option is B

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: \[ \boxed{-16} \]