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If z is a point on the Argand plane satisfying |z - 1| = 1, then (z - 2)/z equals:

1. tan(arg z)
2. cot(arg z)
3. i tan(arg z)
4. none of these

Correct answer: i tan(arg z)

Solution

On the circle |z - 1| = 1 write z = 1 + e^(2i*t); then (z - 2)/z simplifies to i tan(t), and arg z = t, so the value is i tan(arg z).

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