Solve the equation z^4= -i
De Moivre's Theorem
The Attempt at a Solution
I understand how to find the roots by equating modulus and argument but I wanted to ask how do you know which arguments to take? Because I got up to
4*theta = -Pi/2, 3*Pi/2, 7*Pi/2
then I thought that I should take -5*Pi/2 because I thought that the final argument should lie between -Pi and Pi. Is that wrong? Because the answers took 11*Pi/2 instead...
I don't understand. Please help.