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Question

Which of the following expressions is a sixth root of unity?

1. i
2. -1
3. -i
4. All of the above are correct

I appreciate the help.

Answer 1

e^0 i = cos 0 + i sin 0 = 1 that does not help much

e^2 pi i = cos 2pi + i sin 2pi = 1

so
1^(1/6) e^(2 pi/6)i
2 pi/6 = pi/3 = 60 deg
so cos theta + i sin theta
0 deg 1
60 deg
120 deg
180 deg -1
240 deg
300 deg
none of these is along the i axis so i and -i are out
only 2. which is -1 at 180 degrees is in

Answer 2

thank you so much!!!

Answer 3

You are welcome :)