Let $f:C\to C$ and such $$|f(x-y)|=||f(x)-f(y)|,\forall x,y\in C$$ is there $$f(x+y)=f(x)+f(y),\forall x,y\in C$$
I have prove when $x,y\in R$.But for complex,I can't solve it.
is there $f(x+y)=f(x)+f(y)$?
math110
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