Question

If $\left|z\right|=4$ and arg z=$\frac{5\pi }{6}$ then $z=?$

• 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 $-2\sqrt{3}+2i$

We have,

$\left|z\right|=4$

$\arg \left(z\right)=\frac{5\pi }{6}$

Therefore,

$z=\left|z\right|(\cos \left(\frac{5\pi }{6}\right)+i\sin \left(\frac{5\pi }{6}\right))$

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

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

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

Hence, this is the answer.