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0mgl0la

  • 2 years ago

What are the characteristics of a complex number? What is the relationship between a complex number and its conjugate? Describe the usefulness of the conjugate and its effect on other complex numbers.

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  1. lgbasallote
    • 2 years ago
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    wow so many questions

  2. lgbasallote
    • 2 years ago
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    i feel like im in a job interview all over again :/

  3. vf321
    • 2 years ago
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    A complex number is a number which has both a real part a and imaginary part b i, where a and b are elements of the Reals, and i = sqrt(-1).

  4. vf321
    • 2 years ago
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    Now im guessing for the second question that you're having trouble because you don't know what a conjugate is. Is that the case?

  5. AshShade
    • 2 years ago
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    The relationship is that the product of a complex number and it's respective complex conjugate is a real number.

  6. AshShade
    • 2 years ago
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    For number two. ^

  7. vf321
    • 2 years ago
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    Yes. But do you know how to find one?

  8. 0mgl0la
    • 2 years ago
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    ..I still don't understand the last one.

  9. vf321
    • 2 years ago
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    Well it let's you turn complex numbers into reals. This comes in handy in many respects. For instance, in mathematics we often need to make the denominator real. Here's where it comes in: \[\frac{1}{3+i} = \frac{1}{3+i} \times 1 = \frac{1}{3+i} \times \frac{3-i}{3-i} = \frac{3-i}{9+1}\]

  10. vf321
    • 2 years ago
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    But that's a very easy way of answering your question. Aside from "aesthetics" like realizing (?) the denominator, it comes in hand when factoring polynomials. If you find one root for a polynomial that's imaginary, and the polynomial had real coefficients to begin with, then I guarantee you that its conjugate is also a root, since somewhere along the line those two roots had to cancel using the conjugate property you described to make real coefficients for the polynomial.

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