Question

If $z=\frac{{(\sqrt{3}+i)}^{17}}{{(1-i)}^{50}}$, then $amp\left(z\right)$ is equal to

• A. $\frac{2\pi }{3}$
• B. $-\frac{\pi }{3}$
• C. $-\frac{2\pi }{3}$
• D. $None$

Answer 1

The correct option is A $\frac{2\pi }{3}$

$amp\left(z\right)=ta{n}^{-1}\left(\frac{\sin \frac{46\pi }{3}}{cos\frac{46\pi }{3}}\right)$

$=ta{n}^{-1}\left(\tan \frac{46\pi }{3}\right)$

$=ta{n}^{-1}\tan \left(16\pi -\frac{2\pi }{3}\right)$

$=ta{n}^{-1}\left(\tan \left(\frac{2\pi }{3}\right)\right)$

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