Proving z^5 is uniformly continuous on unit ball

samer88
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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


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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].
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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