A.3  Manipulating Complex Numbers and Rational Functions

The complex-conjugate of a sum of two complex numbers is the sum of the conjugate of these numbers. For instance:

This is also valid for the conjugate of a difference, product, or quotient of two numbers, which is the difference, product, or quotient, respectively, of their individual conjugates.

This is useful when manipulating a rational system function $H(z)$ to obtain $H^{\ast }(z)$, as required in Eq. (F.59). For instance, suppose $H(z)\; =\; (z\; -\; 2e^{j4})(z\; -\; 3\; +\; j5)∕(z\; +\; 6e^{-j4})$, then $H^{\ast }(z)\; =\; (z^{\ast }-\; 2e^{-j4})(z^{\ast }-\; 3\; -\; j5)∕(z^{\ast }+\; 6e^{j4})$.