How can I solve complex root problems without using De'Moivre's theorem?

[alwaysconfuse]

Homework Statement

What is the square root of z=-9

Homework Equations

The Attempt at a Solution

Is it possible of me to not use De'Moivre's theorem to solve this question??
Solution :
z= \sqrt{-9}
z=\sqrt{9} x \sqrt{}-1
z=\pm3 i

Will this method be acceptable?? Is this still under the topic complex roots?

 

[lanedance]

be careful with your notation you have written both:
z=-9
and
z=\sqrt{-9}

That said what you have done is ok. For a more general method see below:
https://www.physicsforums.com/showthread.php?t=526970