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December 19th, 2014, 11:47 PM   #1
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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 ???

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December 20th, 2014, 12:28 AM   #2
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$\displaystyle ( \frac{-1}{2} + \frac{i \sqrt{3}}{2} )^3= \frac{-1}{8} + \frac{3i \sqrt{3}}{8} + \frac{9}{8} - \frac{3i \sqrt{3}}{8} = \frac{8}{8} =1$

Nothing is missing.......
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December 20th, 2014, 01:35 AM   #3
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thanks!

i had calculated [-1/2 + i(sqrt 3)/2]^2, instead of [-1/2 + i(sqrt 3)/2]^3

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