Question

Question #ea8c2

Answer 1

Assuming that you mean an imaginary number, this is true.

Explanation:

Essentially, you can't square root a negative number, because if you multiply two negative numbers together you get a positive number. (Try `-5times-5`)
Mathematicians weren't going to let a little thing like impossibility get in their way, so they decided to use imagination.

Basically, we let `sqrt(-1)= i` and then multiply anything by `i` that's imaginary that we want to use. For example, the notation `4i` means 4 times `sqrt(-1)`, or `sqrt(-4)`.

This is very useful when solving quadratic equations for example.

Try solving `x^2-5x+8` -
`(x+5/2)^2 +7/4=0`
`(x+5/2)^2=-7/4`
`x+5/2=sqrt(-7/4)`
now you can't really get the square root of negative `7/4`, so you have to multiply by `i`:
`x+5/2=(sqrt(7)i)/sqrt4`
`x+5/2=(sqrt(7)i)/2`
`x=-5/2+(sqrt(7)i)/2`

graph{x^2-5x+8 [-5, 10, -5, 10]} notice how the graph of this equation doesn't cross the x-axis. This is because it has no real roots as both the roots are imaginary - they have `i` in them.