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Complex conjugate
The conjugate of the complex number z = a + bi is defined as
Explanation
If two complex numbers only differ by the sign of the imaginary part, they are called complex conjugate, or just conjugate. It is determined by definition that
The figure below shows the point z and the conjugate z̅ in the complexe plane.
The absolute square of z is defined as |z|2 = z z̅.
Example 1
You can simplify a fraction by multiplying the whole numerator and the whole denominator with the same conjugate
Example 2
You can write the number 2 with a complex conjugate as