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JEE Advanced Mathematics question

MathematicsComplex NumbersJEE Advanced

If then is

Answer: (A)

Solution

Let . Then

(1+i)(x+iy) = (x-y) + i(x+y), (1-i)(x-iy) = (x-y) - i(x+y).

Equating gives , so with any real number. That is (a). Check: and $(1-i) t(1+i)

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Question ID VK-108051