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Conjugate of a Complex Numbers
Conjugate of a complex number z = a + ib is denoted and defined by = a-ib.
In a complex number if we replace i by -i, we get conjugate of the complex number. is the mirror image of z about real axis on Argand's Plane.
Geometrical representation of conjugate of complex number -
|z| = ||
arg () = - arg (z)
General value of arg ()= 2nΠ P.V. arg(z)
(i) If z = x+y, then x= z+/2, y = z+/2
(ii) z = = z is purely real
(iii) z + = 0 = j is purely imaginary
(iv) ||2 = z
(v) = z
(ix) Imaginary roots of polynomial equations with real coefficient occur is conjugate pairs.
(x) If w=f(z), then = f()