Incremental Complex Products

Algebra Level 5

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

(a+1)(b+1)(c+1)=1 (a+1)(b+1)(c+1) = 1

(a+2)(b+2)(c+2)=2 (a+2)(b+2)(c+2) = 2

(a+3)(b+3)(c+3)=3 (a+3)(b+3)(c+3) = 3

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

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