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anonymous
 4 years ago
Describe the usefulness of the conjugate and its effects on other complex numbers?
anonymous
 4 years ago
Describe the usefulness of the conjugate and its effects on other complex numbers?

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anonymous
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.0. In mathematics, complex conjugates are a pair of complex numbers

anonymous
 4 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
 4 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)

anonymous
 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.
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