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 December 19th, 2014, 11:47 PM #1 Newbie   Joined: Oct 2013 Posts: 4 Thanks: 0 cube roots of unity hi what am i missing here........ one of the cube roots of 1 is cos 120 + i sin120. check: (cos 120 + i sin120)^3 = cos 3600 + i sin360 = 1. however when i do this in cartesian form: cos 120 + i sin120 = -1/2 + i(sqrt 3)/2 check: [-1/2 + i(sqrt 3)/2 ] = -1/2 - i(sqrt 3)/2 as opposed to 1 ??? thanks
 December 20th, 2014, 12:28 AM #2 Senior Member     Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry $\displaystyle ( \frac{-1}{2} + \frac{i \sqrt{3}}{2} )^3= \frac{-1}{8} + \frac{3i \sqrt{3}}{8} + \frac{9}{8} - \frac{3i \sqrt{3}}{8} = \frac{8}{8} =1$ Nothing is missing....... Thanks from not3bad
 December 20th, 2014, 01:35 AM #3 Newbie   Joined: Oct 2013 Posts: 4 Thanks: 0 thanks! i had calculated [-1/2 + i(sqrt 3)/2]^2, instead of [-1/2 + i(sqrt 3)/2]^3

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