Question

What is the square root of this equation?

`x^2`=-16

Answer 1

`x = +-4i`

Explanation:

Given:

`x^2 = -16`

We might say that to solve the equation you should take the square root, which essentially means take the square root of both sides of the equation. The problem with such a statement is that under normal circumstances any non-zero number has two square roots. Those roots may be real or non-real complex roots, but one is minus the other.

In our example we find:

`x = +-4i`

where `i^2 = -1`

That is:

`x = 4i" "` or `" "x = -4i`

So you could say that "the square root of the equation" is the disjunction:

`x = 4i vv x = -4i`

which we abbreviate to:

`x = +-4i`