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. (4.57). For instance, suppose $H(z)=(z-2e^{j4})(z-3+j5)∕(z+6e^{-j4})$, then $H^{\ast }(z)=(z^{\ast }-2e^{-j4})(z^{\ast }-3-j5)∕(z^{\ast }+6e^{j4})$.