Difference between revisions of "Complex conjugate"
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* If a complex number <math>z</math> is a root of a polynomial with real coefficients, then so is <math>\overline z</math>. | * If a complex number <math>z</math> is a root of a polynomial with real coefficients, then so is <math>\overline z</math>. | ||
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+ | Also, The complex conjugate of <math>a + b = a - b</math>. | ||
+ | This edit by codeninja29 | ||
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Revision as of 04:36, 19 December 2018
The conjugate of a complex number is
, denoted by
. Geometrically,
is the reflection of
across the real axis if both points were plotted in the complex plane.
Properties
Conjugation is its own functional inverse and commutes with the usual operations on complex numbers:
.
. (
is the same as
)
. (
is the same as
)
It also interacts in simple ways with other operations on :
.
.
- If
for
,
. That is,
is the complex number of same absolute value but opposite argument of
.
where
is the real part of
.
where
is the imaginary part of
.
- If a complex number
is a root of a polynomial with real coefficients, then so is
.
Also, The complex conjugate of .
This edit by codeninja29
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