Cube Roots of a Complex Number

Author:
James R Olsen
This worksheet graphs a number N and finds the 3 cube roots of N. The roots are are , , and .
GeoGebra Applet
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 N = 1 + 0i (which is the real number 1). 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 1.) Q2. Move N so that 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 N = -1 + 0i (which is the real number -1). 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 -1.) [You can check your answers by checking the three checkboxes to reveal the values.]

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