The complex numbers z_1,z_2,z_3 are the vertices of a triangle. Then the complex number z which makes the triangle into a parallelogram, is

JEE Main Mathematics question

The complex numbers are the vertices of a triangle. Then the complex number which makes the triangle into a parallelogram, is

(A)
(B)
(C)
(D)All of theseCorrect

Answer: (D)

Solution

For a parallelogram, the diagonals bisect each other, so the fourth vertex is (sum of the two vertices at the ends of a diagonal) minus the third vertex. Choosing the diagonal

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Question ID VK-013575