show that the product of a + bi and its conjugate is real number?

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  • 1 decade ago
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    By definition, the conjugate of a + bi is a - bi.

    (a + bi)(a - bi) = a^2 - abi + abi - (bi)^2 = a^2 - (bi)^2

    = a^2 - (b^2)( i^2) = a^2 - (-1)(b^2) since i^2 = -1

    = a^2 + b^2

    If a and b are real, then a^2 + b^2 is also real.

  • 1 decade ago

    a+bi(a-bi)=a^2+b therefore its a real number

    Source(s): no1 is special every1 is
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