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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....... 
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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