Cube Roots of a Complex Number - With Sliders

Author:: James R Olsen

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.]

Cube Roots of a Complex Number - With Sliders

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