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August 13th, 2015, 08:34 AM  #1 
Newbie Joined: Aug 2015 From: London Posts: 1 Thanks: 0  Points on circle argand diagram
I have 3 points in my diagram which are the solutions z^3=2+2i. The solutions ( correct ) are 2^0.5e(Pi/12)i, 2^0.5e(9Pi/12)i and 2^0.5e(7Pi/12)i. Please see the last part of the whole question and if possible help explain it to me  Many thanks https://malletson.files.wordpress.co...question9.pdf https://malletson.files.wordpress.co...question9.pdf 
August 13th, 2015, 01:29 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,704 Thanks: 670 
The three roots determine a circle. The circle is centered at the origin of the complex plane and has a radius of $\displaystyle \sqrt{2}$, so the expression is the sum of the differences between a point on the circle and each of the three roots. This should have a magnitude of 6, for all points on the circle.
Last edited by mathman; August 13th, 2015 at 01:48 PM. 

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