Square Root of Complex Number in Cartesian Form/Examples

Examples of Square Root of Complex Number in Cartesian Form

Example: $i$

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

Example: $2 + 2 i$

$\sqrt {2 + 2 i} = \pm \left({\sqrt {1 + \sqrt 2} + i \sqrt {\sqrt 2 - 1}}\right)$

Example: $3 + 4 i$

$\sqrt {3 + 4 i} = \pm \left({2 + i}\right)$

Example: $-8 + 6 i$

$\sqrt {-8 + 6 i} = \pm \paren {1 + 3 i}$

Example: $5 - 12 i$

$\sqrt {5 - 12 i} = \pm \paren {3 - 2 i}$

Example: $-15 - 8 i$

$\sqrt {-15 - 8 i} = \pm \paren {1 - 4 i}$

Example: $8 + 4 \sqrt 5 i$

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