JEE Main 2022 Mathematics question

Sum of squares of modulus of all the complex numbers z satisfying z̄ = is equal to .

Answer: 2

Solution

Let z = x + iy. The condition z̄ = gives z + z̄ = , i.e. . Separating real and imaginary parts: and . Eliminating gives 2x = −4xy, so x = 0

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Question ID VK-034893