Can some please tell me how to put curly braces around the real part in an equation?

Question

\begin{equation*}
  f \in S\mbox{*} \iff Re({\frac{zf'(z)}{f(z)})>0 
\end{equation*}

Answer 1

Something like this?

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\begin{document}
\begin{equation}
  f \in S^ \iff \mathrm{Re}\left(\biggl{\frac{zf'(z)}{f(z)}\biggr}\right)>0 
\end{equation*}
\end{document}