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Complex conjugate
Fundamental operation on complex numbers / From Wikipedia, the free encyclopedia
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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. That is, if and
are real numbers then the complex conjugate of
is
The complex conjugate of
is often denoted as
or
.
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/6/69/Complex_conjugate_picture.svg/220px-Complex_conjugate_picture.svg.png)
In polar form, if and
are real numbers then the conjugate of
is
This can be shown using Euler's formula.
The product of a complex number and its conjugate is a real number: (or
in polar coordinates).
If a root of a univariate polynomial with real coefficients is complex, then its complex conjugate is also a root.