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anonymous

  • 4 years ago

What is the relationship between a complex number and its conjugate? and what is the usefulness of the conjugate and its effect on other complex numbers?

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  1. mathmate
    • 4 years ago
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    The conjugate of a complex number is that the sign of the complex component is inverted. For example, the conjugate of a+bi is a-bi. One significance is that the product of a complex number with its conjugate is always real.

  2. anonymous
    • 4 years ago
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    so what exactly is the relationship? a real number?

  3. mathmate
    • 4 years ago
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    \( (a+bi)(a-bi)=a^2+b^2 \) The result is a real number for all values of a and b.

  4. anonymous
    • 4 years ago
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    how can i put that into words?

  5. mathmate
    • 4 years ago
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    You can expand the last sentence of my first response. Post your version if you're not sure.

  6. anonymous
    • 4 years ago
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    "the complex number and its conjugate have a set of real numbers in common"

  7. anonymous
    • 4 years ago
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    this is my version

  8. mathmate
    • 4 years ago
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    I would put it as the product of a complex and its conjugate is real. This is useful in "rationalizing" complex numbers where the denominator is a complex number. \[\frac{2+3i}{3+4i} = \frac{(2+3i)(3-4i)}{(3+4i)(3-4i)}=\frac{18+i}{25}\] This facilitates manipulation (such as addition) of complex numbers.

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