Let z denote the complex conjugate of a complex number z and let i = -1 . In the set of complex numbers, the number of distinct roots of the equation z - z^2 = i( z + z^2) is _____.

JEE Advanced 2022 Mathematics question

Let denote the complex conjugate of a complex number and let . In the set of complex numbers, the number of distinct roots of the equation

- = i( +

is .

Answer: 4

Rearranging: . One root is . Otherwise taking moduli, , so

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Question ID VK-033958