Question #ea8c2

1 Answer
Sep 27, 2017

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.