Find the cube roots of i in the form a+bi, where a, b are real numbers.

Write i in terms of an exponential, so i = e^(i pi/2).Then the three roots of i are:z_1 = [e^(i pi/2)]^(1/3) = e^(i pi/6) = sqrt(3)/2 + i/2z_2 = e^[i (pi/6 + 2pi/3)] = e^(i 5pi/6) = -sqrt(3)/2 + i/2z_3 = e^[i (5pi/6 + 2pi/3)] = e^(i -3pi/2) = -i