If (1 + i) (1 + 2i) (1 + ni) = x + iy (Where i = -1 ), then the value of (2) (5) (10) (1 + n^2)

Step-by-step solution

Given (1 + i)(1 + 2i) (1 + ni) = x + iy Taking the conjugate on both sides: (1 - i)(1 - 2i) (1 - ni) = x - iy Multiplying the two equations: ((1 + i)(1 - i))((1 + 2i)(1 - 2i)) ((1 + ni)(1 - ni)) = (x + iy)(x - iy) (1^2 - i^2)(1^2 - (2i)^2) (1^2 - (ni)^2) = x^2 - (iy)^2 Since i^2 = -1 , we get: (1 + 1)(1 + 4) (1 + n^2) = x^2 + y^2 2 5 10 (1 + n^2) = x^2 + y^2 Answer: x^2 + y^2