Proving R is an Equivalence Relation on R^2

jaejoon89 · 2009-08-12T00:15:47+00:00

A relation R on R^2 is defined by (x_{1},y_{1})\mathit{R}(x_{2},y_{2})\;\;\;if\;\;\;x_{1}^{2}+y_{1}^{2}=x_{2}^{2}+y_{2}^{2} How do you show that R is an equivalance relation?

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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Thread 'Solve this problem that involves induction'

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Thread 'Finding the nth roots of a complex number'

Thread 'Solve this problem that involves induction'

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