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Centre and radius of the circle given by a modulus equation in z

This type of question, asked 3 times: 4 May 2023 S2, 15 May 2023 S2, 22 Apr 2025 S1. All 3 questions below, oldest first.

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  1. Question 1

    4 May 2023 S2

    138
    If ∣z1+i∣=2\left|\frac{z}{1+i}\right|=2, where z=x+iy,i=−1z=x+iy, i=\sqrt{-1} represents a circle, then centre 'C' and radius 'r' of the circle are

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  2. Question 2

    15 May 2023 S2

    122
    If the complex number z=x+iyz = x+iy, where i=−1i = \sqrt{-1}, satisfies the condition ∣z+1∣=1|z+1| = 1, then zz lies on

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  3. Question 3

    22 Apr 2025 S1

    136
    If z=x+iyz =x+ iy is a complex number, then the equation ∣z+iz−i∣=3\left| \frac{z+i}{z-i} \right|=\sqrt{3} represents the

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