Let $U,V,W\subset\mathbb C$ be open sets. Let $f:U\to V$ and $g:V\to W$ be [conformal maps](/page/Conformal%20Maps), meaning that $f$ is holomorphic on $U$ with $f'(z)\neq 0$ for every $z\in U$, and $g$ is holomorphic on $V$ with $g'(\zeta)\neq 0$ for every $\zeta\in V$. Then $g\circ f:U\to W$ is conformal on $U$. Moreover, for every $z\in U$,

\begin{align*} (g\circ f)'(z)=g'(f(z))f'(z). \end{align*}