Problem 1781 (difficulty: 6/10)

Let \(\displaystyle F\not\subseteq G\) and \(\displaystyle D\) compex simply connected domains \(\displaystyle a\in F\), and \(\displaystyle f:F\leftrightarrow D\), \(\displaystyle g:G\leftrightarrow D\) conformal bijections such that \(\displaystyle f(a)=g(a)\). Show that \(\displaystyle |f'(a)|>|g'(a)|\).

Give me another random problem!