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For z belonging to C, which of the following equations represents a circle in the Argand plane?

1. |z - 1| + |z + 1| = 3
2. (z - 3 + i)(conjugate of z - 3 - i) = 5
3. 3*|z - 2 + i| = 7
4. |z - 3| = 2

Correct answer: |z - 1| + |z + 1| = 3

Solution

Options 2, 3 and 4 each reduce to |z - centre| = radius (a circle); option 1 is the sum of distances to two foci equal to a constant, which is an ellipse, so it is the odd one out.

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