Find the indicated roots and graph them in the complex plane.

The fifth roots of i

From the graph give the exact roots. (Express θ in radians.)

Question

Find the indicated roots and graph them in the complex plane.

The fifth roots of i

From the graph give the exact roots. (Express θ in radians.)

anonymous · Answer

exp(i (n2pi + pi) /5 )          n=0,1,2,3,4
= exp(i*pi/5), exp(i3*pi/5), exp(i5*pi/5), exp(i7*pi/5), exp(i9*pi/5)
= exp(i*pi/5), exp(i*pi*3/5), exp(i*pi), exp(i*pi*7/5), exp(i*pi*9/5)
These are points on the unit circle at angles of pi/5, 3pi/5, pi, 7pi/5, 9pi/5