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JEE Main · 2024 · 27 Jan 2024 · Shift 1 · Complex Numbers

If

S = {z \in C : ∣ z - i ∣ = ∣ z + i ∣ = ∣ z - 1∣}

, then,

n (S)

is:

(A)1✓ Correct
(B)0
(C)3
(D)2

Answer: (A)

Solution

∣ z - i ∣ = ∣ z + i ∣ = ∣ z - 1∣

says

z

is equidistant from the three non-collinear points

i, - i, 1

. Such a point is unique: the circumcentre of the triangle they form. So

n (S) = 1

.

JEE Main · 2024 · 27 Jan 2024 · Shift 1 · Single correct option

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