What are imaginary numbers?? Why can’t the square root of a negative be real?

Question

What are imaginary numbers?? Why can’t the square root of a negative be real?

In: 2

Answer 1

A positive * a positive is positive, and a negative * a negative is positive. This means that anything times itself is always positive.

So: if anything times itself is *always* positive, what’s the square root of -4? It’s not -2, because -2 * -2 is 4.

In order to solve this, we came up with “the square root of -1 is a thing we’ll call ‘i'”. Now, we can say that the square root of -4 is “the square root of 4 * the square root of -1”, which gives us “2i”.