The simplest answer is to use the polar form of a complex number and use the rules of exponentiation.
Complex number - Wikipedia, the free encyclopedia
This is one of the first things you should have learnt when studying imaginary numbers...
The i is not under the square root.
The title is also quite misleading. You are trying to find the square root of a negative number, not the square root of an imaginary number. It's more complicated when you are trying to find the square root of an imaginary number.