# Math Help - Complex Numbers

1. ## Complex Numbers

How come square root of -2 is written i squareroot 2 but the squareroot of -36 is written 6i ? Is it because -36 is a perfect square and -2 isn't?
Edit also can someone show me an example of writing a quadratic equation with these solutions?
3 + squareroot 5 / 2 , 3 - squareroot 5 / 2 . ?

2. Originally Posted by D@nny
How come square root of -2 is written i squareroot 2 but the squareroot of -36 is written 6i ? Is it because -36 is a perfect square and -2 isn't?
sqrt(-2) = i sqrt(2)

sqrt(-36) = i sqrt(36) = 6i

Edit also can someone show me an example of writing a quadratic equation with these solutions?
3 + squareroot 5 / 2 , 3 - squareroot 5 / 2 . ?
You need to use brackets to make it clear exactly what you mean, but lets suppose these are a=[3+sqrt(5)]/2, and b=[3-sqrt(5)]/2

then one such quadratic equation is:

(x-a)(x-b)=0

Now expanding the left hand side of this we have:

x^2 + (-a-b)x + ab = x^2 + (-6/2)x + (3^2+5)/4 = x^2 - 3x + 7,

x^2 - 3x + 7=0

RonL

3. I just to mention that the square root of a negative number is actually undefined, like I explain in the other thread. But it seems schools do not care.

4. Originally Posted by ThePerfectHacker
I just to mention that the square root of a negative number is actually undefined, like I explain in the other thread. But it seems schools do not care.
Formally speaking I agree. However there is a justifiable use for such a definition so why not teach it?

-Dan