i-th root of i

how??

i-th root of i = i^(1/i) = i^(-i) = 1/(i^i)

euler's formula: cos t + i sin t = e^(i t)
t= pi/2
i = e^(i pi/2)
i^i = [e^(i pi/2)]^i = e^(i*i*pi/2) = e^(-pi/2)

1/(i^i) = 1/[e^(-pi/2)] = e^(pi/2)