Proving z^5 is uniformly continuous on unit ball

[samer88]

Homework Statement

let f be the function defined in the region |z|<1 , by f(z)=z^5. prove that f is uniformly continuous in |z|<1...where z is a complex number

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

Using what basis? It is a fact that if a function is continuous on a closed and bounded set, then it is uniformly continuous on any subset. If you are allowed to use that, it is sufficient to observe that $z^5$ is continuous on [math]|z|\le 5[/math].