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 $-2\sqrt{3}+2i$

Given,

$\left|z\right|=4$ and $argz=\frac{5\pi }{6}$

Now,

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

$Z=4\times \frac{-\left(\sqrt{3}\right)}{2}+i\times 4\times \frac{1}{2}$

$Z=-2\sqrt{3}+2i$