What are the most important things to keep in mind when working with radical equations and complex numbers?

Radical equations are algebraic equations that contain variables under a radical sign, usually a square root. In general, these are variables under nth root symbols. You should not that the solution to radical equations are most likely imaginary or complex number. It happens when you have a term, √-1. which cannot be simplified further. The value of √-1 is just expressed in a variable 'i' which mean imaginary. It cannot be seen on the number line, so these roots are not real. You should note that you treat 'i' just like any variable, and apply the rules of algebra. This means that complex numbers can be simplified using these equalities:

i = √-1
i² = -1
i³ = -i
i⁴ = 1

Hence, an imaginary number can be real once raised to a power that is a multiple of 4. For example, i⁸ = i⁴*i⁴ = 1*1 = 1.