Question

What is the solution of the equation when solved over the complex numbers?

x^2+20=0


x = ____ or x = ____

Answer 1

`x=+i√(20)\approx+4.472i`

`x=-i√(20)\approx-4.472i`

Explanation:

Starting from
`x^2+20=0`, we do
`x^2=-20`, which means
`x=\pm√(-20)`, which can be written as
`x=\pm√((-1)(20))`, which gives us
`x=\pm√((-1))√((20))`, which we know is
`x=\pm i √((20))`, so our solutions are:

`x=+i√((20))`

`x=-i√((20))`

Which can be approximated to:

`x\approx+4.472i`

`x\approx-4.472i`