Question

how to sketch square root of a complex number

Answer 1

The square root is not a well defined function on complex numbers. Because of the fundamental theorem of algebra, you will always have two different square roots for a given number. If you want to find out the possible values, the easiest way is probably to go with De Moivre's formula, that is, converting your number into the form r(cos(θ)+isin(θ)), and then you will get (r(cos(θ)+isin(θ)))1/2=±
√
r
(cos(θ/2)+isin(θ/2)