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Math Help - Conjugate?

  1. #1
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    Conjugate?

    Find the product of sqrt (-15) and its conjugate.

    Ok, so I am not sure how to do this with a square root involved. Any tips?
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by tsmith View Post
    Find the product of sqrt (-15) and its conjugate.

    Ok, so I am not sure how to do this with a square root involved. Any tips?
    \sqrt{-15} = \sqrt{-1}\, \sqrt{15} = i\sqrt{15}

    In this case the conjugate will also be i\sqrt{15}
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  3. #3
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    Quote Originally Posted by tsmith View Post
    Find the product of sqrt (-15) and its conjugate.

    Ok, so I am not sure how to do this with a square root involved. Any tips?
    the conjugate of a+bi is a-bi

    \sqrt{-15} = 0 + (\sqrt{15})i
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  4. #4
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    Quote Originally Posted by e^(i*pi) View Post
    \sqrt{-15} = \sqrt{-1}\, \sqrt{15} = i\sqrt{15}

    In this case the conjugate will also be i\sqrt{15}
    That must be a typo. The conjugate of i\sqrt{15} is -i\sqrt{15}, of course. Generally speaking a product of conjugates, (a+bi)(a-bi)= a^2+ b^2 is the square of the "modulus" of the number. Since |i\sqrt{15}|= |i||\sqrt{15}|=  \sqrt{15}, that product is 15.
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