Where (in the complex plane) are the solutions of an equation?

First of all: a polynomial of degree N has exactly N roots (in the complex plane) [ref]
Second: since for every root there is also its complex-conjugate [ref], we can only have some combinations...

Degree	Roots	Possible Combinations
1	1	Real Root
2	2	Real Roots, or 2 Complex Roots
3	3	Real Roots, or 1 Real and 2 Complex Roots
4	4	Real Roots, or 2 Real and 2 Complex Roots, or 4 Complex Roots
etc etc!

Eventually, complex numbers are defined like this.