Question

Let z be a complex number number such that |z| = 4 and arg(z) = $\frac{5\pi }{6}$, then z equals-

• A. -2$\sqrt{3}$ +2i
• B. 2$\sqrt{3}$ +2i
• C. 2$\sqrt{3}$ -2i
• D. $\sqrt{3}$ +i

Answer 1

The correct option is A -2$\sqrt{3}$ +2i

Let $z=r(\cos \theta +i\sin \theta )$.
Then $r=4,\theta =\frac{5\pi }{6}$

$\therefore z=4[\cos \frac{5\pi }{6}+i\sin \frac{5\pi }{6}]$

$=4[-\frac{\sqrt{3}}{2}+\frac{i}{2}]$
$=-2\sqrt{3}+2i$