The zeros of the complementary error function

We show that the complementary error function, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\text{erfc} (z)= \frac{2}{\sqrt{\pi}}\int_z^{\infty}{e^{-s^2} \text{d}s}$\end{document}, has no zeros in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\text{D}= \left\{ z : \frac{3}{4} \ \pi \le Arg z \le\frac{5}{4} \ \pi \right\}$\end{document}.