Question

Which expression is a sixth root of -1+i√3?
a.2^(1/6)(cos(300) + isin(300))
b.2^(1/6)(cos(60) + isin(60))
c.2^(1/6)(cos(90) + isin(90))
d.2^(1/6)(cos(20) + isin(20))

Answer 1

the solution is
\[2^{1/6} (\cos \frac{120 +360k}{6} + i \sin \frac{120 +360k}{6})\]
for k = 0,1,2,3,4,5