Prove that if $|f| + |g| \equiv c$ ($c\in \Re$) in set $Ω\subseteq C$ where $f,g$ holomorphic in Ω then $f\equiv a$ , $g\equiv b$ where $a,b\in C$. Well the real problem was to show it for $\sum_{i=1}^{n}|f_{i}| \equiv c$ but I think i should starting by proving it for 2 of them.(This was once given to us on an exam as the only problem in it and it was valuated with 100% of the grade)
2026-03-28 17:40:20.1774719620
$|f| + |g| \equiv c$ in set Ω where $f,g$ holomorphic in Ω
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