SOLUTION: finding the nth root of a complex number (16i)^1/4

Question 1178763: finding the nth root of a complex number
(16i)^1/4
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Use deMoivre's Theorem on the last form to find the 4th roots

(1) Find the "primary" root. To find the nth root of a number in a*cis(theta) form, take the nth root of a, and divide the angle theta by n.

(2) Find the other roots. The n n-th roots of a number all have the same magnitude, and they are distributed around the complex plane in intervals of (2pi)/n.

The 4th roots are at intervals of pi/2 in the complex plane. Starting with the "primary" root of 2*cis(pi/8), the four 4th roots of 16i are

2cis(pi/8)
2cis(5pi/8)
2cis(9pi/8)
2cis(13pi/8)

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