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Mathematics Forum
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| Author | Message / Information |
| The Riemann Hypothesis Quote | Reply | | Complex Cube Roots of Unity posted on: 4/28/2006 10:42:24 PM There aren't enough challenges on this forum. Show that the complex cube roots of unity satisfy the equation: a^2- a + 1 = 0 Hence show that: (a^2 + 1)^6 = 1 |
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prasannasagar_m
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Complex Cube Roots of Unity
replied on: 12/15/2006 12:12:41 AM consider the equation x^3 = 1. => x^3-1=0 => (x-1)(x^2-x+1)=0 => x=1 is one root which is the real root. so the other roots should satisfy the equation x^2-x+1=0 these are the complex roots. x^2+1=x => (x^2+1)^6 = x^6 x^6=(x^3)^2= (1)^2=1 As simple as that! |
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