Solution: We have, n = 4 with:
wn = cos (2 p)k/ n + isin(2 pk)/n
For k = 0, 1, 2 and 3 then,
The first root::
w0 = cos(0) + isin(0) = 1
The second root:
w1 = cos (p/2) + isin(p/2) = 1i = i
The third root:
w2 = cos (p) + isin(p) = -1
And the fourth root:
w3 = cos(3 p/2) + isin(3p/2) = -1i = -i
All of which can be checked using the accompanying diagram which is part of the problem solution.
Note the roots correspond to successive increases of the angle by p/2 = 90 degrees:
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