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JEE Advanced 2023 · Paper 1

JEE Advanced 2023 Mathematics question on Complex Numbers and Quadratic Equations

Let zz be a complex number satisfying ∣z∣3+2z2+4zˉ−8=0|z|^3+2z^2+4\bar{z}-8=0, where zˉ\bar{z} denotes the complex conjugate of zz. Let the imaginary part of zz be nonzero.

Match each entry in List-I to the correct entries in List-II.
List-I
(P) ∣z∣2|z|^2 is equal to
(Q) ∣z−zˉ∣2|z-\bar{z}|^2 is equal to
(R) ∣z∣2+∣z+zˉ∣2|z|^2+|z+\bar{z}|^2 is equal to
(S) ∣z+1∣2|z+1|^2 is equal to
List-II
(1) 1212
(2) 44
(3) 88
(4) 1010
(5) 77
  1. A.
    (P)→(1)(P)\rightarrow(1) \quad (Q)→(3)(Q)\rightarrow(3) \quad (R)→(5)(R)\rightarrow(5) \quad (S)→(4)(S)\rightarrow(4)
  2. B.
    (P)→(2)(P)\rightarrow(2) \quad (Q)→(1)(Q)\rightarrow(1) \quad (R)→(3)(R)\rightarrow(3) \quad (S)→(5)(S)\rightarrow(5)
  3. C.
    (P)→(2)(P)\rightarrow(2) \quad (Q)→(4)(Q)\rightarrow(4) \quad (R)→(5)(R)\rightarrow(5) \quad (S)→(1)(S)\rightarrow(1)
  4. D.
    (P)→(2)(P)\rightarrow(2) \quad (Q)→(3)(Q)\rightarrow(3) \quad (R)→(5)(R)\rightarrow(5) \quad (S)→(4)(S)\rightarrow(4)
Show answer

Correct option: B

[JEE Advanced 2023 · Paper 1]

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