JEE Main 2024 Mathematics question

Mathematics Complex Numbers JEE Main 2024

If z = 1/2 – 2i is such that |z + 1| = αz + β(1 + i), i = √−1 and α, β ∈ ℝ, then α + β is equal to-

(A)–4
(B)2
(C)–1
(D)3Correct

Answer: (D)

Solution

|z + 1| = |3/2 − 2i| = 5/2. So 5/2 = α(1/2 − 2i) + β(1 + i) = (α/2 + β) + i(−2α +

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Question ID VK-016902