This worksheet graphs a number N and finds the 4 fourth roots of N. The roots are are , , , and .

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.]