Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

0mgl0la Group Title

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.

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. lgbasallote Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    wow so many questions

    • 2 years ago
  2. lgbasallote Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i feel like im in a job interview all over again :/

    • 2 years ago
  3. vf321 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    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).

    • 2 years ago
  4. vf321 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    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?

    • 2 years ago
  5. AshShade Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    The relationship is that the product of a complex number and it's respective complex conjugate is a real number.

    • 2 years ago
  6. AshShade Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    For number two. ^

    • 2 years ago
  7. vf321 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes. But do you know how to find one?

    • 2 years ago
  8. 0mgl0la Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ..I still don't understand the last one.

    • 2 years ago
  9. vf321 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    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: \[\frac{1}{3+i} = \frac{1}{3+i} \times 1 = \frac{1}{3+i} \times \frac{3-i}{3-i} = \frac{3-i}{9+1}\]

    • 2 years ago
  10. vf321 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    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.

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.