Answer:
2^60.
Step-by-step explanation:
You can do this using deMoivres theorem.
First convert to Polar form:
(-1+i(root 3))^60
r = √((-1)^2 + (√3)^2)
= √(1 + 3)
= 2.
So sin Ф = √3/2
Ф = 2π/3 - as the angle is in the second quadrant ( real part is -1)
So in polar form we have:
[2(cos2π/3 + i sin2π/3 )]^60
Bu de Moivres theorem this is
2^60(cos2π/3* 60 + i sin2π/3* 60)
= 2^60(cos(120π/3) + i sin(120π/3)
= 2^60(cos40π + i sin 40π)
= 2^60(1 + i*0)
= 2^60.
