Abstract
We investigate the count and placement of zeros of a generalized complex harmonic trinomial \(P_{c}(z).\) In particular, we prove that \(P_{c}(z)\) has \((n+2k+j+1)\) number of zeros. Also, we obtain that sense-preserving and sense-reversing areas of \(P_{c}(z)\) lie in annular regions that enclose the critical curve of \(P_{c}(z)\) . At last we locate the zeros of \(P_{c}(z)\) and obtain annular sectors containing zeros of \(P_{c}(z).\) We demonstrate our findings with examples and figures.
