Aus Online Mathematik Brückenkurs 2

We can determine the number's magnitude directly using the distance formula

\displaystyle \begin{align} & \left| \sqrt{10}+\sqrt{30}i \right|=\sqrt{\left( \sqrt{10} \right)^{2}+\left( \sqrt{30} \right)^{2}}=\sqrt{10+30} \\ & =\sqrt{40}=\sqrt{4\centerdot 10}=2\sqrt{10} \\ \end{align}

In addition, the number lies in the first quadrant and we can therefore determine the argument using simple trigonometry.

The polar form is

\displaystyle 2\sqrt{10}\left( \cos \frac{\pi }{3}+i\sin \frac{\pi }{3} \right)