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mckayla_04

Describe the usefulness of the conjugate and its effects on other complex numbers?

  • 2 years ago
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  1. partyrainbow276
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    i got it hold on

    • 2 years ago
  2. partyrainbow276
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    The conjugate it's used to solve operations with complex numbers.Conjugation of a complex number describes an axial symmetry of the complex plane. To conjugate a complex number, reflect its position through. Conjugation of a complex number describes an axial symmetry of the complex plane. To conjugate a complex number, reflect its position through the real axis. This geometric significance is used a lot

    • 2 years ago
  3. partyrainbow276
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    . In mathematics, complex conjugates are a pair of complex numbers

    • 2 years ago
  4. partyrainbow276
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    done

    • 2 years ago
  5. Callum29
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    Any complex number may be written as \[a+ib\] where \[a,b \in \mathbb{R}\] The complex conjugate of \[a+ib\] is \[a-ib\] The effect of the conjugate can be seen under the various operations: \[a+ib - (a-ib) = 2ib \in \mathbb{C}\] \[a+ib + (a-ib) = 2a \in \mathbb{R}\] \[(a+ib)(a-ib) = a^2 +b^2 \in \mathbb{R}\] \[\frac{a+ib}{a-ib} = \frac{(a+ib)^2}{(a-ib)(a+ib)} = \frac{a^2+2abi-b^2}{a^2+b^2} = \frac{1}{a^2+b^2}([a^2-b^2] + i[2ab])\]

    • 2 years ago
  6. Callum29
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    Notice that \[\sqrt{(a+ib)(a-ib)} = \sqrt{a^2+b^2} = |a+ib|\] (the modulus)

    • 2 years ago
  7. apoorvk
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    A complex multiplied by its conjugate is reduced to a real no. So, it helps while rationalizing, especially the denominators.

    • one year ago
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