Replace each occurrence of ( sqrt{-1} ) with ( i )
Use ( i^2 = -1 )
Rewrite ( sqrt{-a} ) as ( sqrt{a},i ) for ( a>0 )
Separate real and imaginary parts
Simplify powers of ( i ) using the cycle
( i^1 = i )
( i^2 = -1 )
( i^3 = -i )
( i^4 = 1 )
Repeat every 4 powers
Write complex numbers in the form ( a+bi )
Factor out ( i ) from negative square roots when possible
Convert expressions involving ( sqrt{-n} ) into ( sqrt{n},i )
Keep ( i ) in the denominator only if required, then rationalize if needed