Number of Zeros of an equation Why is it that the equation $z^5=0$ has five zeros, seeing as
 $z=0$ is the only solution? (When $z$ is a complex number) The context for this is Rouche's theorem.

The equation has five zeros, but they are not unique. We say that the solution $z=0$ has multiplicity five, meaning there are five such solutions.
This all relates to the Fundamental theorem of Algebra which says that a polynomial of degree $n$ has exactly $n$ roots (counting multiplicity). This could also be formulated as "a polynomial of degree $n$ has $\leq n$ unique roots", but this claim is less strong.
