Let z be a complex number with non-zero imaginary part. If 2 + 3z + 4z^2 2 - 3z + 4z^2 is a real number, then the value of |z|^2 is _____.

JEE Advanced 2022 Mathematics question

Let be a complex number with non-zero imaginary part. If

is a real number, then the value of is .

Answer: 0.5

Dividing numerator and denominator by : the expression is with . A Möbius map of this form is real exactly when is real (or

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Question ID VK-033957