For any complex number 𝑤 = 𝑐 + 𝑖𝑑, let arg(w) ∈ (−𝜋, 𝜋], where 𝑖 = √−1 . Let 𝛼 and 𝛽 be real numbers

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JEE Advanced 2021 Mathematics paper 1 Solution

For any complex number 𝑤 = 𝑐 + 𝑖𝑑, let arg(w) ∈ (−𝜋, 𝜋], where 𝑖 = √−1 . Let 𝛼 and 𝛽 be real numbers such that for all complex numbers 𝑧 = 𝑥 + 𝑖𝑦 satisfying arg (𝑧+𝛼/𝑧+𝛽) =𝜋/4, the ordered pair (𝑥, 𝑦) lies on the circle 𝑥2 + 𝑦2 + 5𝑥 − 3𝑦 + 4 = 0 Then which of the following statements is (are) TRUE ?
(A) 𝛼 = −1 (B) 𝛼𝛽 = 4 (C) 𝛼𝛽 = −4 (D) 𝛽 = 4

Complex number Question in JEE Advanced 2021 Maths paper 1

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