Imaginary Number

An imaginary number is the mathematician’s hacky solution to calculating square roots of negative numbers.

Imaginary unit

Silly mathematicians! They couldn’t figure out a real solution to the following innocent-looking expression:

$$\sqrt{-1}$$

And so, they made something up:

$$\sqrt{-1}=i$$

Where $i$ is the imaginary unit. It is fundamentally, axiomatically, equal to the square root of $-1$ by definition. Why? Because the mathematicians were getting desperate, that’s why.

More formally, an imaginary number can be defined as taking the form of $bi$, where $b$ is a real number.

Why does $b$ have to be real?

Because if $b$ was imaginary, it would have an $i$ in it. Multiplying two $i$s would cancel out the square roots and you’d just get $-1$, ya silly potato.