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The Riemann Hypothesis






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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
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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