Question

If \( z = e^{2\pi i / 3} \), then \( 1 + z + 3z^2 + 2z^3 + 2z^4 + 3z^5 \) is equal to:

• A. \( -3e^{\pi i / 3} \)
• B. \( 3e^{\pi i / 3} \)
• C. \( 3e^{2\pi i / 3} \)
• D. \( -3e^{2\pi i / 3} \)
• E. \( 0 \)

Hint:

When you see $e^{2\pi i / n}$, you are working with $n$-th roots of unity. Always group the terms in sets of $n$ to exploit the fact that their sum is zero.

Answer 1

The Correct Option is A