question_answer

A rectangle is constructed in the complex plane with its sides parallel to the axes and its centre is situated at the origin. If one of the vertices of the rectangle is \[a+ib\sqrt{3}\], then the area of the rectangle is

A) \[ab\sqrt{3}\]

B) \[2ab\sqrt{3}\]

C) \[3ab\sqrt{3}\]

D) \[4ab\sqrt{3}\]

Correct Answer: D

Solution :

Area of required rectangle = 4×area of \[OABC\] \[=4\times a\times b\sqrt{3}=4ab\sqrt{3}\].