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Locus |z - z1| = |z - z2| is a straight line (perpendicular bisector)

This type of question, asked 4 times: 2 May 2023 S2, 10 May 2024 S1, 20 Apr 2025 S1, 19 May 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    2 May 2023 S2

    125
    If P(x,y)P(x,y) denotes z=x+iyz=x+iy and ∣z−1z+2i∣=1\left|\frac{z-1}{z+2i}\right|=1, then the locus of P is

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  2. Question 2

    10 May 2024 S1

    129
    If w=zz−13iw=\frac{z}{z-\frac{1}{3}i} and ∣w∣=1|w|=1, z lies on

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  3. Question 3

    20 Apr 2025 S1

    129
    The equation ∣z+1−i∣=∣z−1+i∣|z+ 1 -i| = |z- 1 +i| represents a (where z is a complex number)

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  4. Question 4

    19 May 2026 S2

    52
    If ∣z−5i∣=∣z+3∣|z - 5i| = |z + 3|, where zz is a complex number, then the equation of the locus of zz in Cartesian coordinates is ...

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