Polar form of $$$3 + 4 i$$$

Find the polar form of $$$3 + 4 i$$$.

The standard form of the complex number is $$$3 + 4 i$$$.

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 $$$a = 3$$$ and $$$b = 4$$$.

Thus, $$$r = \sqrt{3^{2} + 4^{2}} = 5$$$.

Also, $$$\theta = \operatorname{atan}{\left(\frac{4}{3} \right)} = \operatorname{atan}{\left(\frac{4}{3} \right)}$$$.

Therefore, $$$3 + 4 i = 5 \left(\cos{\left(\operatorname{atan}{\left(\frac{4}{3} \right)} \right)} + i \sin{\left(\operatorname{atan}{\left(\frac{4}{3} \right)} \right)}\right).$$$

$$$3 + 4 i = 5 \left(\cos{\left(\operatorname{atan}{\left(\frac{4}{3} \right)} \right)} + i \sin{\left(\operatorname{atan}{\left(\frac{4}{3} \right)} \right)}\right) = 5 \left(\cos{\left(\left(\frac{180 \operatorname{atan}{\left(\frac{4}{3} \right)}}{\pi}\right)^{\circ} \right)} + i \sin{\left(\left(\frac{180 \operatorname{atan}{\left(\frac{4}{3} \right)}}{\pi}\right)^{\circ} \right)}\right)$$$A