Complex Numbers
Roots of Unity
Premium Question
Grade 11
Question:
If $\omega = e^{2\pi i/5}$, then $\prod_{k=1}^4(1 - \omega^k)$ equals:
(1) $1$
(2) $3$
(3) $5$
(4) $10$
Step-by-Step Solution
Key Concept: Factor $x^5 - 1 = (x - 1)(x - \omega)(x - \omega^2)(x - \omega^3)(x - \omega^4)$. Divide by $(x - 1)$ and evaluate at $x = 1$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)