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Math Help - find the product and its conjugate-complex numbers

  1. #1
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    Question find the product and its conjugate-complex numbers

    Can someone explain how I would solve this?

    Find the product of the number and its conjugate.

    square root of negative 15.
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  2. #2
    Super Member malaygoel's Avatar
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    The product of a complex number and its conjugate is equal to the square of the modulus of the complex number.

    Here,
    complex number is \sqrt{-15} or i\sqrt{15}
    What is the modulus of this number?
    What is conjugate of this number?
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  3. #3
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    Quote Originally Posted by kikitaiszcraQk View Post
    Find the product of the number and its conjugate.
    \left( {a + bi} \right)\overline {\left( {a + bi} \right)}  = \left( {a + bi} \right)\left( {a - bi} \right) = \left( a \right)^2  - \left( {bi} \right)^2  = a^2  + b^2
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  4. #4
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    I don't understand how you can get "a" and "bi" from a negative square root.
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  5. #5
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    Quote Originally Posted by malaygoel View Post
    The product of a complex number and its conjugate is equal to the square of the modulus of the complex number.

    Here,
    complex number is \sqrt{-15} or i\sqrt{15}
    What is the modulus of this number?
    What is conjugate of this number?
    The modulus of this number would be 15 so the product is 15^2=225?
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  6. #6
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    Quote Originally Posted by kikitaiszcraQk View Post
    The modulus of this number would be 15 so the product is 15^2=225?
    correct ...

    (0 + i\sqrt{15})(0 - i\sqrt{15}) = -i^2(\sqrt{15})^2 = -(-1)(15) = 15
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