An algebra problem by megh choksi

Algebra Level 3

find the sum of all the possible values of the complex number \(d\) such that there exists values of \(a, b \) satisfying

1) \(\{(a + 1)(b - 1) + (b + 1)(a - 1)\}d + (a - 1)(b - 1) = 0\)
2) \(d( a + 1)( b + 1) - ( a - 1)(b - 1) =0\)
3) Define \(\mathcal{ A = \{ { \frac{a + 1}{a - 1} , \frac{b + 1}{b - 1}}\} }\) and \(\mathcal{B = \{{\frac{2a}{a + 1} , \frac{ 2b}{ b + 1} }\}}\). We have \(A \bigcap B \neq \emptyset\).

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