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Q.
Represent $z=1+i\sqrt{3}$ in the polar form.
Complex Numbers and Quadratic Equations
Solution:
Let $1 = r cos \theta, \sqrt{3}=rsin \theta$
By squaring and adding, we get
$r^{2}\left(cos^{2}\,\theta+sin^{2}\,\theta\right)=4 $
i.e., $r=\sqrt{4}=2$
Therefore, $cos\,\theta=\frac{1}{2}$,
$sin\theta=\frac{\sqrt{3}}{2}$,
which gives $\theta =\frac{\pi}{3}$
Therefore, required polar form is
$z=2\left(cos\frac{\pi}{3}+i\, sin\frac{\pi}{3}\right)$