complex conjugate
1
7.7
- noun
- /ˈkɒmplɛks ˈkɒndʒʊɡət/
- Specialized
:
conjugado complejo
- The complex conjugate of the number 3 + 4i is 3 - 4i.
Examples
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"Googly amplitudes are simply the complex conjugates of the corresponding MHV trees.
Academic text (2004) -
So this is equal to the integral DXC complex conjugate F star G.
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It's just a little exercise, the complex conjugate of a product.
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This is the complex conjugate of this, and X is real.
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It's just taking the complex conjugate and these two guys are equal.
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This looks like we're going to have complex conjugates and a real root as well.
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And the property of real numbers is that when you take the complex conjugate, nothing happens because I goes to minus I.
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plus their complex conjugates.
Academic text (2004) -
In advanced mathematics, the complex conjugate is used to simplify expressions involving complex numbers.
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When solving equations, we often work with the complex conjugate to ensure the results are real.
Surface Forms
Morphology
The adjective 'complex' points to complex numbers and 'conjugate' carries the general sense of a paired counterpart, so a learner could infer this refers to the corresponding paired complex number. However, the specific rule (identical real part with the imaginary part sign reversed) is a technical mathematical convention not deducible from the everyday meanings of the constituents, making the relation only partially transparent.
Etymology
Complex conjugate is like a mirror: take a complex number a + bi and flip the sign of the 'imaginary part' to get its conjugate a - bi. So, they match in the 'real part' but have opposite imaginary parts, and that is why a complex conjugate is the partner number that often gives a real result when you multiply them.