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.}`