Match the statements of Column I with these in Column II. [Note : Here $z$ takes values in the complex plane and $Im (z)$ and $Re (z)$ denote respectively, the imaginary part and the real part of $z$ ]

Question

Match the statements of Column I with these in Column II. [Note : Here z takes values in the complex plane and Im ( z ) and Re ( z ) denote respectively, the imaginary part and the real part of z ]

TestHub · Accepted Answer

(A) z is equidistant from the points i ∣ z ∣ and − i ∣ z ∣ , whose perpendicular bisector is Im ( z ) = 0 . (B) Sum of distance of z from ( 4 , 0 ) and ( − 4 , 0 ) is a constant 10 , hence locus of z is ellipse with semi-major axis 5 and focus at ( ± 4 , 0 ) , a e = 4 . ∴ e = 5 4 ​ (C) ∣ z ∣ ≤ ∣ w ∣ + ​ w 1 ​ ​ = 2 5 ​ < 3 (D) ∣ z ∣ ≤ ∣ w ∣ + ​ w 1 ​ ​ = 2 ∴ Re ( z ) ≤ ∣ z ∣ ≤ 2

Mathematics - Complex Number Question with Solution | TestHub

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JEE Advanced (2028)