Question

The value of \( (1 + \omega)^3 \), where \( \omega = e^{i 2\pi/3} \) is

• A. \( 1280 \)
• B. \( 128 \)
• C. \( 0 \)
• D. \( 1 \)

Hint:

For cube roots of unity, \( 1 + \omega + \omega^2 = 0 \).

Answer 1

The Correct Option is C

Step 1: Use the properties of cube roots of unity.
For \( \omega = e^{i 2\pi / 3} \), \( \omega^3 = 1 \) and \( (1 + \omega)^3 \) simplifies to 0 based on the fact that \( 1 + \omega + \omega^2 = 0 \).
Step 2: Conclusion.
The correct answer is (C), 0.