Approximation Several Zeroes of a Class of Periodical Complex Functions

Abstract

This paper discussed the number of zeros of the complex function $F:C \rightarrow C$ defined by $$F(Z)=\sum\limits_{k=1}^n(a_k cos(kZ)+b_k sin(kZ))+α_0+α_1 Im(z)+\cdots+α_m(Im(Z))^m.$$