Complex Analysis, Video #24 (Complex Arithmetic, Part 24).
Main Topic: finding the nth roots of a complex number and visualizing them to see that they form a regular polygon in the complex plane.
Review animation from previous video to visualize the set of 12th roots of any nonzero complex number. Add an extra animation parameter that allows us to visualize mth roots for integer values of m from 2 to 12. Write a formula for the set of nth roots, first in exponential polar form, then in trigonometric polar form. Find the 5th roots of z = -1 + sqrt(3)*i. The modulus of z is 2 and the principal value of the argument is 2*pi/3. The modulus of the 5th roots is the non-negative (real) 5th root of 2. The arguments are 2*pi/15, 8*pi/15, 14*pi/15, 20*pi/15, and 26*pi/15.