Fourth Roots of a Complex Number

Author:
James R Olsen
Topic:
Angles, Function Graph, Root
This worksheet graphs a number N and finds the 4 fourth roots of N. The roots are are , , , and .
GeoGebra Applet
Experiment: Manipulate N (click and drag) and see the relationships involving the 4 fourth 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 four fourth roots:
  • angle,
  • modulus (distance from the origin), and
  • a + bi.
(You found the four fourth roots of 1.) Q2. Move N so that N = -1 + 0i (which is the real number -1). What are the values for the four fourth roots:
  • angle,
  • modulus (distance from the origin), and
  • a + bi.
(You found the four fourth roots of -1.) Q3. Move N so that N = 0 + 1i (which is the number i). What are the values for the four fourth roots:
  • angle,
  • modulus (distance from the origin), and
  • a + bi (estimate).
(You found the four fourth roots of i.) [You can check your answers by checking the three checkboxes to reveal the values.]

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