JEE Advanced 2022 Mathematics question

Let denote the complex conjugate of a complex number . If is a non-zero complex number for which both real and imaginary parts of

( +

are integers, then which of the following is/are possible value(s) of ?

Answer: (A)

Solution

With : . If its real and imaginary parts are integers , then must be an integer that is a sum of two squares, i.e. . (A) $ =

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Question ID VK-034018