ABCD is a square, vertices being taken in the anticlockwise sense. If A represents the complex number z and the intersection of the diagonals is the origin then

JEE Advanced Mathematics question

ABCD is a square, vertices being taken in the anticlockwise sense. If A represents the complex number and the intersection of the diagonals is the origin then

(A)B represents the complex number Correct
(B)D represents the complex number
(C)B represents the complex number
(D)D represents the complex number Correct

Answer: (A),(D)

Solution

The diagonals of a square are equal, bisect each other at right angles, so OA=OB=OC=OD=|z| and consecutive vertices subtend at O. Going anticlockwise A → B → C → D, each vertex is the previous one rotated by about O, i.e. multiplied by :

B=iz, C==-z, D==-iz .

So (a) a

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Question ID VK-108131