Elementary Relationships
From the above definitions, one can quickly verify
![\begin{eqnarray*}
z+\overline{z} &=& 2 \, \mbox{re}\left\{z\right\} \\
z-\overl...
...left\{z\right\} \\
z\overline{z} &=& \left\vert z\right\vert^2.
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/mdft/img204.png)
Let's verify the third relationship which states that a complex number multiplied by its conjugate is equal to its magnitude squared:
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