Difference between revisions of "Complex conjugate"
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==Properties== | ==Properties== | ||
− | Conjugation is its own [[inverse]] and commutes with the usual [[operation]]s on complex numbers: | + | Conjugation is its own [[Function/Introduction#The_Inverse_of_a_Function | functional inverse]] and [[commutative property | commutes]] with the usual [[operation]]s on complex numbers: |
* <math>\overline{(\overline z)} = z</math> | * <math>\overline{(\overline z)} = z</math> | ||
* <math>\overline{(w \cdot z)} = \overline{w} \cdot \overline{z}</math> | * <math>\overline{(w \cdot z)} = \overline{w} \cdot \overline{z}</math> |
Revision as of 10:05, 15 October 2006
The complex conjugate of a complex number is the complex number
.
Geometrically, if is a point in the complex plane,
is the reflection of
across the real axis.
Properties
Conjugation is its own functional inverse and commutes with the usual operations on complex numbers:
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
.
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