If |z_1|=|z_2|=|z_3|=1 and z_1,z_2,z_3 are represented by the vertices of an equilateral triangle then

JEE Advanced Mathematics question

If and are represented by the vertices of an equilateral triangle then

(A)Correct
(B)
(C)Correct
(D)none of these

Answer: (A),(C)

Solution

The vertices are at distance 1 from the origin, so O is the circumcentre. In an equilateral triangle the circumcentre is the centroid, so , i.e. — (a) ✓.

More explicitly, going round the triangle, , (or with swapped). Then -

See the full step-by-step solution

Create a free account to read the complete working (4 steps), and practise questions like this in a timed test.

Create a free account

Question ID VK-108135