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mitchelsewbaran

  • 3 years ago

Find the product of the complex number and its conjugate. 3 + 3i

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  1. whpalmer4
    • 3 years ago
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    The complex conjugate of a+bi is a - bi. The product of a complex number and its conjugate will be \[(a+bi)(a-bi)=a^2-abi+abi+b^2i^2=a^2-b^2\]

  2. mitchelsewbaran
    • 3 years ago
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    9 - 9i?

  3. whpalmer4
    • 3 years ago
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    Sorry, I made a sign mistake, that should be \[(a+bi)(a-bi)= a^2-abi+abi-b^2i^2=a^2+b^2\]

  4. whpalmer4
    • 3 years ago
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    So you have a = 3, b = 3, and the result is 3^2+3^2=18

  5. whpalmer4
    • 3 years ago
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    the i terms cancel out, and the i^2 term just changes sign because i^2= -1

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