First slide

Geometry of complex numbers

Question

If z lies on the circle $|z - 1| = 1$ then $\frac{z - 2}{z}$ equals

Moderate

A

0
B

2
C

-1
D

none of these

Solution

Note that $|z - 1| = 1$ represents a circle with the segment joining z = 0 and z = 2 +0i as a diameter.
If z lies on the circle, then $\frac{z - 2}{z - 0}$ is purely imaginary. ( since the angle at z is $\frac{π}{2}$ )

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