Then, besides at most m - 1 even number counting multiplicities, real or

complex conjugate zeros, the function [C.sub.[sigma]](z) - f(z) has only real zeros with the following distribution properties:

Then the eigenvalues of A are real or occur in

complex conjugate pairs.

The use of a multi-harmonic load based on an arbitrarily width modulated transmission line [19] provides a precise control over the position of the pair of

complex conjugate poles created after reaching the condition expressed by (2) [7].

An indication is given in Figure 2, based on the a priori knowledge that the real part of both

complex conjugate roots is -0.5.

where [Q.sub.i] is the Q-factor of the i-th

complex conjugate pole pair; n is the number of these pole pairs; [Q.sub.max] is specified Q-factor limit.

Assume that [lambda]E - A is stable and that the complex shift parameters appear in

complex conjugate pairs {[[tau].sub.k], [[tau].sub.k+1] = [[bar.[tau]]].sub.k]}.

94-95) asserts that

complex conjugate roots can exist only if all the coefficients are real.

(this would not be the case if the [z.sub.i] were arbitrary instead of real or

complex conjugate).

two-dimensional x-y plot of the quadratic equation does not reveal the location of the

complex conjugate roots, and the interested student might well be forgiven for asking, "Where exactly are the roots located and why can't I see them?" In the author's experience, this sort of question is hardly ever raised--or answered satisfactorily--in school Years 11 or 12, or in undergraduate mathematics courses.

If the orthogonal iteration process described in [section]3.1 is applied to a matrix B that has a

complex conjugate pair of eigenvalues, then [Q.sup.T.sub.j] B[Q.sub.j] converges to a block triangular form.

ZH represents the Hermitian transpose of

complex conjugate of X

where, [mathematical expression not reproducible] represent the

complex conjugate operator (Demanent, 2015).