In this section, we will present an algorithm that helps us learn, in a finite number of steps, if the following complex polynomial:

has all its zeros inside the unit disk; that is, in the subset:

For that, we introduce the polynomials and *P**(*z*) represented as follows:

obtained by conjugating^{3} the coefficients of *P*(*z*) without conjugating the variable and

obtained by conjugating and inversing the order of the coefficients of *P*(*z*). The polynomial *P*(z)* is then called the reciprocal polynomial of *P*(*z*).

EXAMPLE 10.4.- the polynomial *P*(*z*) = (2 + *j*)z^{3} + 3*z* admits, for reciprocal polynomial *P**(*z*) = 3*z*^{2} + (2 − *j*).

COMMENT 10.1.- the reciprocal polynomials *P**(*z*) and satisfy the following equality:

Now, from the polynomial *P*_{N}(*z*) = *P*(*z*), we construct a family of

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