Question

Let z be a complex number such that $|z|=4$ and arg $z=\frac{5\pi }{6}$. What is z equal to?

• 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 C $-2\sqrt{3}+2i$

$Letz=|z|(cos\theta +isin\theta )$

$\therefore z=4(cos\left(\frac{5\pi }{6}\right)+isin\left(\frac{5\pi }{6}\right))$

$\therefore z=4(\frac{-\sqrt{3}}{2}+\frac{1}{2}i)$

$\therefore z=-2\sqrt{3}+2i$