Complex Numbers

Algebra Level 4

Let a,b,c a,b,c be complex numbers satisfying

{(a+1)(b+1)(c+1)=1(a+2)(b+2)(c+2)=2(a+3)(b+3)(c+3)=3 \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) (a+4)(b+4)(c+4) .

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