Question

If -1+$\sqrt{-3}$=r$e^{i\theta }$, then $\theta$ is equal to

• A. $\frac{\pi }{3}$
• B. -$\frac{\pi }{3}$
• C. $\frac{2\pi }{3}$
• D. -$\frac{2\pi }{3}$

Answer 1

The correct option is C

$\frac{2\pi }{3}$

Here -1+$\sqrt{-3}$=r$e^{i\theta }$ $\Rightarrow$ -1+$i\sqrt{3}$=r$e^{i\theta }$

=rcos$\theta$=-1 And rsin$\theta$=$\sqrt{3}$

Hence tan$\theta$=-$\sqrt{3}$ $\Rightarrow$ tan$\theta$=tan$\frac{2\pi }{3}$.Hence $\theta$=$\frac{2\pi }{3}$