Square Root of Complex Number in Cartesian Form/Examples/i

Example of Square Root of Complex Number

 * $\sqrt i = \pm \left({\dfrac {\sqrt 2} 2 + \dfrac {\sqrt 2} 2 i}\right)$

Proof
As $2 x y = 1$ it follows that the two solutions are:


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