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Q.
If $z_1=\sqrt{3}+i \sqrt{3}$ and $z_2=\sqrt{3}+i$, then $\left(\frac{z_1}{z_2}\right)$ lies in quadrant ...A... . Here, A refers to
Complex Numbers and Quadratic Equations
Solution:
$\frac{z_1}{z_2} =\frac{\sqrt{3}+i \sqrt{3}}{\sqrt{3}+i} $
$ =\frac{\sqrt{3}+i \sqrt{3}}{\sqrt{3}+i} \times \frac{\sqrt{3}-i}{\sqrt{3}-i}=\frac{3+3 i-\sqrt{3} i+\sqrt{3}}{4} $
$ =\left(\frac{3+\sqrt{3}}{4}\right)+\left(\frac{3-\sqrt{3}}{4}\right) i$
which is represented by a point in I quadrant.