Complex Numbers

Algebra Level 5

Let \( a,b,c \) be complex numbers satisfying

\[ \begin{cases} (a+1)(b+1)(c+1) = 1\\ (a+2)(b+2)(c+2) = 2\\ (a+3)(b+3)(c+3) = 3\end{cases} \]

Find \( (a+4)(b+4)(c+4) \).

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