Ask your own question, for FREE!
Mathematics
OpenStudy (anonymous):

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

OpenStudy (anonymous):

i got it hold on

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

done

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (apoorvk):

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

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
TheShootingStar100: Hi I' new here I need help earning more medals how do I get more
23 minutes ago 11 Replies 1 Medal
TheShootingStar100: How do I earn more fans
2 hours ago 8 Replies 1 Medal
Coperdom: how to do the sum of num
6 hours ago 1 Reply 0 Medals
Coperdom: Help
8 hours ago 0 Replies 0 Medals
Coperdom: Help
6 hours ago 6 Replies 0 Medals
Sailor: stress art again bc ive absolutely had a terrible day
7 hours ago 10 Replies 2 Medals
0mega: Phantom of the Opera drawing
8 hours ago 11 Replies 4 Medals
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!