Chapter 9.7, Problem 1GCE

To determine

To approximate the cube roots of $1$ .

Answer to Problem 1GCE

  $x=1,-\frac{1}{2}+i\frac{\sqrt{3}}{2},-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

Explanation of Solution

Given:

The cube roots of $1$ .

Calculation:

The cube roots of $1$ can be approximated using the graphing calculator as follows-

  $\begin{array}{l}{x}^3-1=0\\ x^3=1\\ x=\sqrt[3]{1}\\ x=1\end{array}$

  $x=1,-\frac{1}{2}+i\frac{\sqrt{3}}{2},-\frac{1}{2}-i\frac{\sqrt{3}}{2}$