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In the Argand plane, describe the locus of points z satisfying |z - (2 + 3i)| = 1.

1. A circle of radius 1 centred at (2, 3)
2. A circle of radius 2 centred at (2, 3)
3. A straight line through (2, 3)
4. A circle of radius 1 centred at (-2, -3)

Correct answer: A circle of radius 1 centred at (2, 3)

Solution

|z - (2+3i)| = 1 means z is always at distance 1 from the point (2, 3), which is a circle of radius 1 centred there.

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