A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
Describe the usefulness of the conjugate and its effects on other complex numbers?
anonymous
 5 years ago
Describe the usefulness of the conjugate and its effects on other complex numbers?

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The 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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0. In mathematics, complex conjugates are a pair of complex numbers

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Any complex number may be written as \[a+ib\] where \[a,b \in \mathbb{R}\] The complex conjugate of \[a+ib\] is \[aib\] The effect of the conjugate can be seen under the various operations: \[a+ib  (aib) = 2ib \in \mathbb{C}\] \[a+ib + (aib) = 2a \in \mathbb{R}\] \[(a+ib)(aib) = a^2 +b^2 \in \mathbb{R}\] \[\frac{a+ib}{aib} = \frac{(a+ib)^2}{(aib)(a+ib)} = \frac{a^2+2abib^2}{a^2+b^2} = \frac{1}{a^2+b^2}([a^2b^2] + i[2ab])\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Notice that \[\sqrt{(a+ib)(aib)} = \sqrt{a^2+b^2} = a+ib\] (the modulus)

apoorvk
 4 years ago
Best ResponseYou've already chosen the best response.0A complex multiplied by its conjugate is reduced to a real no. So, it helps while rationalizing, especially the denominators.
Ask your own question
Sign UpFind 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
 Engagement 19 Mad Hatter
 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.