Question: what is the square root of negative 1

Amy Mason answered on 13 Nov 2024:

i.

This is what is called an imaginary number. The definition is literally that it is the number that squared makes -1.
It is really useful for a lot of calculations, like solving quadratic equations.

Some people don’t like imaginary numbers because they don’t obviously correspond to something in the real world. But I would argue that negative numbers don’t correspond to the real world either – you can’t actually take 8 apples away from 2 apples, because you cannot keep removing apples when there are none left.

We can think of negative numbers as the reverse of addition. -6 apples means that if you add 6 apples, there are no apples left. In the same way, we can think of imaginary numbers as the reverse of squaring.