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Let A and B be two complex numbers (treated as points in the Argand plane) satisfying A/B + B/A = 1. Together with the origin O, the points A and B are the vertices of which type of triangle?

1. an equilateral triangle
2. an isosceles triangle which is not equilateral
3. a scalene triangle
4. a right angled triangle

Correct answer: an equilateral triangle

Solution

A/B + B/A = 1 gives A² - AB + B² = 0, which is the standard condition for the origin and A, B to be the vertices of an equilateral triangle.

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