Question

If modulus and amplitude of a complex number are $2$ and $\frac{2\pi }{3}$ respectively, then the number is

• A. $1i\sqrt{3}$
• B. $1+i\sqrt{3}$
• C. $-1+i\sqrt{3}$
• D. $-1i\sqrt{3}$

Answer 1

The correct option is C $-1+i\sqrt{3}$

If $r$ and $\theta$ are modulus and amplitude of a complex number.
then $z=r(\cos \theta +i\sin \theta )$
$\Rightarrow z=2(\cos \frac{2\pi }{3}+i\sin \frac{2\pi }{3})$
$\therefore z=-1+i\sqrt{3}$
Hence, option C.