Toconclude that each complex nth root lies on a circle with center at the origin and its radiusis
Explanation of Solution
Given Information:
Any
Calculation:
Now as it is given that any complex number z that satisfies the equation
Thus, n distinct complex nth roots of
,are given by the formula
Where
Now depending upon a new value of k, a new complex root is found out, but as magnitude
This means that the points corresponding to each root lie on a circle with center at the origin and radius
Furthermore, the arguments of these roots are
Which is a constant term that means that these points are equally spaced on the circle boundary.
Chapter 9 Solutions
Precalculus
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