Square Root of Complex Number in Cartesian Form/Examples/8 + 4 root 5 i

Example of Square Root of Complex Number in Cartesian Form

 * $\sqrt {8 + 4 \sqrt 5 i} = \pm \paren {\sqrt {10} + \sqrt 2 i}$

Proof
As $2 x y = 4 \sqrt 5$ it follows that the two solutions are:


 * $\sqrt {10} + \sqrt 2 i$
 * $-\sqrt {10} - \sqrt 2 i$