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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:

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

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