Cube Roots of a Complex Number - With Sliders

This worksheet graphs a number N, using sliders for the angle and modulus, and finds the 3 cube roots of N. The roots are are , , and .
Experiment: Manipulate N (click and drag) and see the relationships involving the 3 cube roots. Uncheck the three boxes showing the values for the numbers. Questions: Q1. Move N so that the angle is 0 and the modulus is 1 (which is the real number 1). What are the values for the three cube roots:
  • angle,
  • modulus (distance from the origin).
(You found the three cube roots of 1.) Q2. Move N so that the angle is 90 and the modulus is 1 (N = 0 + 1i, which is the number i). What are the values for the three cube roots:
  • angle,
  • modulus (distance from the origin), and
  • a + bi.
(You found the three cube roots of i.) Q3. Move N so that the angle is 150 and the modulus is 1. What are the values for the two square roots:
  • angle,
  • modulus (distance from the origin)
[You can check your answers by checking the three checkboxes to reveal the values.]