Question

Use the following equation to answer the questions below: x^ 4 = 1 (Note: Factoring more than once may be needed to discover solutions.)A. What are the real solutions to the equation above?B. What are the imaginary solutions to the equation above?

Answer 1

Given:

$x^4=1$

Taking square root on both sides, We have

$x^2=\pm1$

A)

$x^2=1$$x=\pm1$

-1 and 1 are the real solutions of the given equation.

B)

$x^2=-1$$x=\pm i$$x=i,-i$$i\text{ and -i are the imaginary solutions of the given equation.}$