Why Does This Mathematical Expression Equal Zero?

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SUMMARY

The mathematical expression in question equals zero due to the properties of vectors representing the vertices of a regular polygon in the complex plane. When the points are evenly distributed, their vector sum results in zero. This holds true unless the variable 'c' is a multiple of 'q/r', which causes all vertices to converge to a single point, negating the vector sum. The discussion highlights the geometric interpretation of complex numbers and their behavior in summation.

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  • Knowledge of vector addition in a geometric context
  • Familiarity with regular polygons and their properties
  • Basic principles of exponential functions in mathematics
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Baggio
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URGENT: Why does this tern = 0??

Can anyone tell me why the term in the bracket = 0??

where i= root -1 and all vars are integers

I'm at a loss :-/
 

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Each exponential in the sum represents a point in the complex plane and if you look at the terms carefully you will see that the set of points comprise the vertices of a regular polygon. Think of each point as being a vector from the origin to the given point. Being the vertices of a regular polygon, the vectors must add to zero! That is, unless c is a multiple of q/r in which case all the vertices converge to a single point.
 
Hehe, ok I think that makes sense.. thanks
 

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