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.]