Definitions for complex conjugate
com·plex con·ju·gate

Princeton's WordNetRate this definition:0.0 / 0 votes

1. complex conjugatenoun

   either of two complex numbers whose real parts are identical and whose imaginary parts differ only in sign

WiktionaryRate this definition:0.0 / 0 votes

1. complex conjugatenoun

   Of a complex number x, the complex number formed by changing the sign of the imaginary part: The complex conjugate of a + bi is a - bi.

WikipediaRate this definition:0.0 / 0 votes

1. Complex conjugate

   In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. For example, (if a and b are real, then) the complex conjugate of a + b i {\displaystyle a+bi} is a − b i . {\displaystyle a-bi.} In polar form, the conjugate of r e i φ {\displaystyle re^{i\varphi }} is r e − i φ {\displaystyle re^{-i\varphi }} . This can be shown using Euler's formula. The product of a complex number and its conjugate is a real number: a 2 + b 2 {\displaystyle a^{2}+b^{2}} or r 2 {\displaystyle r^{2}} in polar coordinates. Complex conjugates are important for finding roots of polynomials. According to the complex conjugate root theorem, if a complex number is a root to a polynomial in one variable with real coefficients (such as the quadratic equation or the cubic equation), so is its conjugate.

ChatGPTRate this definition:0.0 / 0 votes

1. complex conjugate

   The complex conjugate of a complex number is obtained by changing the sign of its imaginary part. If a complex number is expressed as a + bi, where a and b are real numbers and i is the imaginary unit, its complex conjugate is a - bi.

WikidataRate this definition:0.0 / 0 votes

1. Complex conjugate

   In mathematics, complex conjugates are a pair of complex numbers, both having the same real part, but with imaginary parts of equal magnitude and opposite signs. For example, 3 + 4i and 3 − 4i are complex conjugates. The conjugate of the complex number where and are real numbers, is For example, An alternative notation for the complex conjugate is . However, the notation avoids confusion with the notation for the conjugate transpose of a matrix, which can be thought of as a generalization of complex conjugation. The star-notation is preferred in physics, where dagger is used for the conjugate transpose, while the bar-notation is more common in pure mathematics. If a complex number is represented as a 2×2 matrix, the notations are identical. Complex numbers are considered points in the complex plane, a variation of the Cartesian coordinate system where both axes are real number lines that cross at the origin, however, the -axis is a product of real numbers multiplied by +/- . On the illustration, the -axis is called the real axis, labeled Re, while the -axis is called the imaginary axis, labeled Im. The plane defined by the Re and Im axes represents the space of all possible complex numbers. In this view, complex conjugation corresponds to reflection of a complex number at the x-axis, equivalent to a 180 degree rotation of the complex plane about the Re axis.

Matched Categories

1. • Complex Number

How to pronounce complex conjugate?

1. Alex

   US English

   David

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   Mark

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   Daniel

   British

   Libby

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   Mia

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   Australian

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   Neerja

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   South African

How to say complex conjugate in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of complex conjugate in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of complex conjugate in Pythagorean Numerology is: 4

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=complex conjugate
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Complex_Conjugate
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Complex_Conjugate
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=complex conjugate