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
JC
Related Maths IB answers
All answers ▸How do I solve the equation "2cos(x) = sin(2x), for 0 ≤ x ≤ 3π"?
What is de Moivre's theorem?
Finding complex numbers using DeMoivre's Theorem
The sum of the first n terms of an arithmetic sequence is Sn=3n^2 - 2n. How can you find the formula for the nth term un in terms of n?