مرکز منطقه ای اطلاع رساني علوم و فناوري - Zeros of f(z) = (az-b)<sup>n</sup>pm (cz-d)<sup>n</sup>

DocumentCode :

808136

Title :

Zeros of f(z) = (az-b)ⁿpm (cz-d)ⁿ

Author :

Oraizi, Homayoon

Author_Institution :

Syracuse University, Syracuse, NY, USA

Volume :

Issue :

fYear :

1972

fDate :

4/1/1972 12:00:00 AM

Firstpage :

259

Lastpage :

261

Abstract :

The zeros of $f(z) = (az - b)^{n} \\pm (cz - d)^{n}$ are found to lie on a circle of radius $|(ad - cb)/(|a|^{2} - |c|^{2})|$ with its center at $z = (a^{\\ast }b - c^{\\ast }d)/(|a|^{2} - |c|^{2})$ , where $a, b, c$ , and $d$ are complex numbers and $n$ is assumed real. When $|a| = |c|$ the locus of the zeros is a straight line perpendicular to the line joining the points $b/a$ and $b/c$ and intersecting it at $z = 0.5(b/a + d/c)$ . The zeros are found analytically and constructed geometrically.