Answer to Question #44096 in Complex Analysis for ch

Question

hey, i wanna know step by step how sqrt(-2i) = sqrt(2)*e^(-i*pi/4) = (1-i)

is it necessary to change it to polar form first to get to 1-i ?

and when solving w^2= (-1+sqrt3 i)/2 how does the argument get tan^-1(-sqrt3)=2pi/3

shouldn´t it be tan^-1(-2sqrt3/2) if the formula for argument is arctan(y/x) ?

thnx