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Complex Numbers

Section: Mathematics

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Question : 10

Total: 36

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(‌

, the ordered pair (x,y) lies on the circle x2+y2+5x−3y+ 4=0.
Then which of the following statements is (are) TRUE?

[JEE Adv 2021 P1]

α=−1
αβ=−4
αβ=−4
β=4

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