Complex Analysis: Properties of Line Integrals

tarheelborn
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Homework Statement



Demonstrate that \int_{-\gamma} f(z)|dz|=\int_{\gamma} f(z)|dz| where \gamma is a piecewise smooth path and f is a function that is continuous on |\gamma|.


Homework Equations





The Attempt at a Solution



This proof seems like it should be very simple, but I am not sure it is really saying that it's just turning a path around to go in the opposite direction. Could someone please help me out? Thanks.
 
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Consider the substitution u= -z.
 

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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