Question

Use square roots to solve the equation x ^ 2 = - 25 over the complex numbers. Select any solutions that apply A.-5 B. -5i C. -5i^2 D.5i

Answer 1

B.
`-5i`

D.
`5i`

Explanation:

Remember that the imaginary unit is equal to:

`i^2 = -1`

And getting the square root in both sides of the equation we get:

`i = √(-1) \quad \land \quad -i = √(-1)`

The with our expression we develop of the next way:

`x^2 = -25\\x = √(-25)`

However in the real numbers doesn't exist solution for such operation then you use the complex numbers for represent the operation.

`x = 5i \quad \land \quad x = -5i`

In this occasion we use
`i` and
`-i` because both represent a negative square root, so our final answer is:

B and D