Does sqrt(-2i) = 1-i or i-1

both 1-i or i-1 when squared give - 2i

so both are square roots

but when we need to compute sqrt(-2i) this is the principal sqrt and and as per wiki the principal sqrt is defined to be

if z = r e^it then z^(1/2) = r^(1/2)e^(it/2)

-2i = 2 e^i(- pi/2) (note that that angle should be between (-pi to pi] that is pi is inculded and not -pi

so sqrt(-2i) = sqrt(2) e^(-pi/4)i = sqrt(2)( cos (-pi/4) +i sin (-pi/4)) = 1 -i