Question 632217: Please tell how to graphically locate the nth roots of a complex number, given the location of one of the nth roots. Thanks!! Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! The n roots of a number will be located in a circle, equally spaced at angles of
For example, if A is one of the 6th roots of a number, the other 5 roots are at the ends of the green spokes, all spaced at angles . That is because
if two of the roots are and
the nth power of that is
That means that the angle and are co-terminal, meaning that for some k integer. --> --> --> -->
so the angles are spaced apart,
like spokes of a wheel with n spokes.
