Determine the square roots of without converting it to the trigonometric form, given that .
First, simplify the fraction by multiplying the numerator and denominator by the complex conjugate of the denominator.
Recalling that leads to
Now, express as where and are real numbers. Then,
Now, expand the brackets and simplify, recalling again that .
Compare real and imaginary parts on both sides of the equation.
Rearranging the second equation gives
Substituting into the first equation gives
Substituting into the first equation gives .
So, the solution is: .