Roots of a complex number.

Let $u$ be a complex number and $n$ a natural number ($n \geq 2$ ). An $n^{th}$ root of $u$ is a complex number $z$ such that $z^n = u$ .

Theorem 1.5.1   Every non zero complex number has exactly $n$ distinct $n^{th}$ roots.

The proof of this theorem is given at the beginning of the next subsection.