Question

The principal argument of the complex number $z = \frac{1 + \sin \frac{\pi}{3} + i \cos \frac{\pi}{3}}{1 + \sin \frac{\pi}{3} - i \cos \frac{\pi}{3}}$ is:

• A. $\frac{\pi}{3}$
• B. $\frac{\pi}{6}$
• C. $\frac{2\pi}{3}$
• D. $\frac{\pi}{2}$
• E. $\frac{\pi}{4}$

Hint:

Any complex number of the form $\frac{1 + \bar{w}}{1 + w}$ where $|w|=1$ will have an argument related to the argument of $w$. Specifically, if $w = \cos \alpha - i \sin \alpha$, the result simplifies beautifully into a single exponential term.

Answer 1

The Correct Option is B