Assume that \(z_0\), \(z_1, \dots, z_n\) belong to an angular region bounded by two rays emanating from the origin, \(\sigma_k (z_0, \dots, z_n) = \sum z_0^{j_0} z_1^{j_1}, \dots, z_n^{j_n}\), \(j_0+j_1 + \cdots + j_n =k\), \(j_s\), \(s=0,1, \dots,n\) being nonnegative integers, stands for a symmetric polynomial, \[ \sigma_k (z,z_1, \dots, z_n) = \sum^k_{m=0} \sigma_m(z_1, \dots, z_n) z^{k-m} {\overset{def}=} P_k(z). \] For fixed \(\varphi, \alpha, \alpha >0\) we set \(D_\varphi (\alpha) = \{z: \varphi< \arg z < \varphi + \alpha\} \). The author established several results concerning the distribution of zeros and univalence. The results have fairly complicated forms. One of the simplest results is as follows: For \(z_s\), \(s = 1,2, \dots,n\) arbitrarily fixed in \(\overline {D_\varphi} (2\pi/k)\), the polynomial \(P_k(z)\) is univalent in \(D_\varphi (2\pi/k)\).