Conjugate of a complex number:
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The conjugate of the complex number z = a + ib is described to be a - ib and is shown by . In another words  is the mirror image of z in the real axis.
If z = a + ib, z + = 2 a ( real),
z -= 2 ib ( imaginary )
and 
Also 
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Properties of Conjugate:
=> 
=> |z| = ||
=> z + =2Re(z). z - = 2i Im(z).
If z is completely real z = . whenever we have to define a complex number completely real we take this property.
=> If z is completely imaginary z + =0, whenever we have to define that a complex number is completely imaginary we take this property.
=> In general, 
=>
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