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unscientific
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Homework Statement
Let z1, ... zn be the set of n distinct solutions to the equation
zn = a
where a is a complex number.
(a) By considering distinct solutions as the sides of a polygon in an Argand diagram show that these sum to zero.(b) Hene find the sum of the squares of these solutions. For the case n = 5 sketch the polygon traced out by these successive squared values in the Argand plane.
The Attempt at a Solution
Of course this can be easily solved by doing summation of geometric series, but this isn't a typical question...
I managed to show that the sum of sides = 0 algebraically. This can be shown by using vectors as well (red arrows) that starting from point z1 you will arrive back at z1, implying the overall change = 0.
But, how do i relate each side of the polygon to one solution? Is there a bijection somewhere?