# Polar Form of a Complex Number Calculator

The calculator will find the polar form of the given complex number, with steps shown.

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Find the polar form of $$\sqrt{3} + i$$$. ## Solution The standard form of the complex number is $$\sqrt{3} + i$$$.

For a complex number $$a + b i$$$, the polar form is given by $$r \left(\cos{\left(\theta \right)} + i \sin{\left(\theta \right)}\right)$$$, where $$r = \sqrt{a^{2} + b^{2}}$$$and $$\theta = \operatorname{atan}{\left(\frac{b}{a} \right)}$$$.

We have that $$a = \sqrt{3}$$$and $$b = 1$$$.

Thus, $$r = \sqrt{\left(\sqrt{3}\right)^{2} + 1^{2}} = 2$$$. Also, $$\theta = \operatorname{atan}{\left(\frac{1}{\sqrt{3}} \right)} = \frac{\pi}{6}$$$.