Question

IF $z_1=\sqrt{3}+i\sqrt{3}$ and $z_2=\sqrt{3}+i$ then the complex number $\frac{z_1}{z_2}$ lies in the quadrant number :

• A. I
• B. II
• C. III
• D. IV

Answer 1

The correct option is A I

$z_1=\sqrt{3}+i\sqrt{3}=\sqrt{7}{e}^{\frac{10}{4}}$
$z_2=\sqrt{3}+i={2e}^{\frac{10}{6}}$
$\Rightarrow \left|\frac{z_1}{z_2}\right|=\frac{\sqrt{3}}{\sqrt{2}}$ and $\frac{z_1}{z_2}=\frac{6}{12}=\frac{1}{2}$
$\therefore \frac{z_1}{z_2}$ lies in $1$ quadrant