Question

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

x² + 27=0
Enter your answers, as exact values, in the boxes.
X =
or x =

Answer 1

When you encounter the square root of a negative number, you enter the realm of imaginary numbers. In this case, the solution to the equation x^2-27=0 would be x = ±√27i.

Answer 2

x = - 3i
`√(3)` or x = 3i
`√(3)`

Explanation:

note that
`√(-1)` = i

given

x² + 27 = 0 ( subtract 27 from both sides )

x² = - 27 ( take square root of both sides )

`√(x^2)` = ±
`√(-27)` , that is

x = ±
`√(9(-1)(3))`

= ± (
`√(9)` ×
`√(-1)` ×
`√(3)` ) = ± 3i
`√(3)`

x = - 3i
`√(3)` or x = 3i
`√(3)`