Question

If $(1-i\sqrt{3}{)}^2(z\left)\right(4i)=(1+i\sqrt{3})$, then $Ampz$ is

• A. $\pi$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{3}$
• D. $0$

Answer 1

Answer: (B)

$\frac{\pi }{2}$

$(1-i\sqrt{3}{)}^2(z\left)\right(4i)=(1+i\sqrt{3})$
$\Rightarrow 04iz(1+i\sqrt{3})=\frac{1+i\sqrt{3}}{2}\Rightarrow z=\frac{0+i}{8}=\frac{i}{8}$
$\therefore$ Amp of $z$ or argument of $z={\tan }^{-1}\left(\frac{1/8}{0}\right)$
$\therefore$ Argument of $z=\frac{\pi }{2}$.