The required quadratic equation has roots 1 + i and 1 - i.

=> [x - (1 + i)]*[x - (1 - i)] = 0

=> [x - 1 - i][x - 1 + i] = 0

=> x^2 - x + xi - x + 1 - i - xi + i + 1 =0

cancel the common terms

=> x^2 - 2x + 2 = 0

**Therefore the required equation is x^2 - 2x + 2 = 0.**

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