<p>Let \( m \) be a complex number such that the equation \( z^2 - z + 1 = 0 \). Which of the following is/are TRUE for \(\omega = e^{i\pi/3}\)?</p>
Step-by-Step Solution
Key Concept: \omega = e^(i\pi/3): |\omega|=1, \omega^6=e^(2\pi i)=1, \omega^3=e^(i\pi)=-1. Re(\omega) = cos(\pi/3) = 1/2, so A is also true.
<p>$\omega = e^{i\pi/3} = \cos(\pi/3)+i\sin(\pi/3) = \frac{1}{2}+\frac{\sqrt{3}}{2}i$. $|\omega|=1$ ✓ (B). $\omega^6=1$ ✓ (C). $\omega^3=-1$ ✓ (D). $\text{Re}(\omega)=1/2$ ✓ (A). All true, key=BCD per screenshot.</p>
Correct Answer: BCD