Find the values of:
The answer is:
cos(pi*sqrt(3)[1/2+2k]) + i.sin(pi*sqrt(3)[1/2+2k]), for any integer k.
keywords: de moivres, de moivre's
this is a neat application of de moivre's formula; indeed, this should remind you of how to extract roots of complex numbers! as a first step you would need to write the base of the exponent in polar form, so
i = 0 + 1i = cos (pi/2) + i sin (pi/2)
but the effect of ...
De Moivre's theorem is applied. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.