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\documentclass[UTF8]{ctexart}
\usepackage{amsmath}
\usepackage{cases}
\begin{document}
\begin{subnumcases} {\label{weqn} w\equiv}
0 & for $c = d = 0$\label{wzero}\\
\sqrt{|c|}\,\sqrt{\frac{1 + \sqrt{1+(d/c)^2}}{2}} & for $|c| \geq |d|$ \\
\sqrt{|d|}\,\sqrt{\frac{|c/d| + \sqrt{1+(c/d)^2}}{2}} & for $|c| < |d|$
\end{subnumcases}
Then, using $w$ from eq.~(\ref{weqn}), the square root is
\begin{subnumcases}{\label{sqrteqn} \sqrt{c+id}=}
0\,, & $w=0$ (case \ref{wzero})\\
w+i\frac{d}{2w}\,, & $w \neq 0$, $c \geq 0$ \\
\frac{|d|}{2w} + iw\,, & $w \neq 0$, $c < 0$, $d \geq 0$ \\
\frac{|d|}{2w} - iw\,, & $w \neq 0$, $c < 0$, $d < 0$
\end{subnumcases}
\end{document}