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Math Help - Complex Numbers

  1. #1
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    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 . ?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by D@nny View Post
    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,

    so the quadratic simplifies to:

    x^2 - 3x + 7=0

    RonL
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  3. #3
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    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.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    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
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