Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mckayla_04

  • 2 years ago

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

  • This Question is Closed
  1. partyrainbow276
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    i got it hold on

  2. partyrainbow276
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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

  3. partyrainbow276
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    . In mathematics, complex conjugates are a pair of complex numbers

  4. partyrainbow276
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    done

  5. Callum29
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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: \[a+ib - (a-ib) = 2ib \in \mathbb{C}\] \[a+ib + (a-ib) = 2a \in \mathbb{R}\] \[(a+ib)(a-ib) = a^2 +b^2 \in \mathbb{R}\] \[\frac{a+ib}{a-ib} = \frac{(a+ib)^2}{(a-ib)(a+ib)} = \frac{a^2+2abi-b^2}{a^2+b^2} = \frac{1}{a^2+b^2}([a^2-b^2] + i[2ab])\]

  6. Callum29
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Notice that \[\sqrt{(a+ib)(a-ib)} = \sqrt{a^2+b^2} = |a+ib|\] (the modulus)

  7. apoorvk
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    A complex multiplied by its conjugate is reduced to a real no. So, it helps while rationalizing, especially the denominators.

  8. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.