Originally Posted by
FailingTrig 1. z(1/3) = r^(*1/3) e^(i*pi/2/3)
= cos(pi/6) + i*sin(pi/6)
= squareroot(3/4) + i/2
2. z(1/3) = r^(*1/3) e^(i*(pi/2 + 2*pi)/3)
= cos(5*pi/6) + i*sin(5*pi/6)
= -squareroot(3/4) + i/2
3. z(1/3) = r^(*1/3) e^(i*(pi/2 + 4*pi)/3)
= cos(3*pi/2) + i*sin(3*pi/2)
= 0 - i
Is that correct?
A friend of mine says its supposed to be
k = 0 ==> i^(1/3) = cos(π/6) + i sin(π/6) = (√3 + i)/2
k = 1 ==> i^(1/3) = cos(5π/6) + i sin(5π/6) = (-√3 + i)/2
k = 2 ==> i^(1/3) = cos(3π/2) + i sin(3π/2) = -i.
How do i figure this out =/