Polar Representation of Sinusoidal Functions

StrongForce
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Homework Statement



What would the geometric explanation of exp(-i*x) be?

Homework Equations



Exp(-i*x), i being (-1)^1/2

The Attempt at a Solution



I'm pretty sure this is just a circle, created clockwise? Just want to check.
 
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The magnitude of e^{-i\,x} is 1, so it represents a unit circle with center (0,0).

If x varies on [0,2\,pi) the circle is created clockwise.
 
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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