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If z ≠ 1 and z²/(z − 1) is real, then the point represented by the complex number z lies on:

1. either on the real axis or on a circle passing through the origin.
2. on a circle with centre at the origin.
3. either on the real axis or on a circle not passing through the origin.
4. on the imaginary axis.

Correct answer: either on the real axis or on a circle passing through the origin.

Solution

The expression z²/(z − 1) being real implies that the complex number z must satisfy certain conditions related to its argument and magnitude, which geometrically corresponds to points either lying on the real axis or on a circle that intersects the origin.

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