# Is i^2 = -1?

## Question:

Is {eq}i^2 = -1 {/eq}?

## Complex Numbers

When working in mathematics, we often work only with real numbers. However, this is only a small set of all of the possible numbers that we can work with. Complex numbers are numbers of the form {eq}a + bi {/eq}, where {eq}i = \sqrt{-1} {/eq}. If {eq}b = 0 {/eq}, this is a real number, so all real numbers are also complex numbers.

Yes.

Recall that the imaginary unit is defined as {eq}i = \sqrt{-1} {/eq}. What would happen if we squared both sides of this expression?

{eq}i = \sqrt{-1}\\ i^2 = \sqrt{-1}^2\\ i^2 = \sqrt{-1}\cdot \sqrt{-1} = -1 {/eq}

Therefore, this statement is true.