# MandysNotes

Sunday, 01 May 2011 20:58

## The Complex Conjugate

By  Gideon
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Two complex numbers of the form:

$z_+ = x + iy ,$

and,

$z_- = x - iy ,$

are called Complex Conjugates.

In other words, if

$z = x + iy ,$

then $\bar{z} ,$the complex conjugate of $z ,$is:

$\bar{z} = x - iy .$

The real part of a complex number can always be recovered by the formula:

$Re(z) = \frac{z + \bar{z} }{2} = x ,$

and the imaginary part by the formula:

$Im(z) = \frac{z - \bar{z} }{2i} = y .$