Express the four fourth roots of 1/2 + �ã3/2 i
Do you mean the four roots of
1/2 + (sqrt3)/2 i ?
That can be written as
e^[i (pi/3 + 2n pi)]
where n is an integer.
For the four fourth roots, take 1/4 of
(pi/3 + 2n pi) with n = 0, 1, 2 and 3. For higher values of n, the roots repeat themselves.
The first root will be
e^(i pi/12)
= cos (pi/12) + i sin (pi/12)
= 0.96593 + 0.25882 i