IIT JEE , AIEEE Forum - Mathematics , Algebra

prateek.agarwal

4. If z₁, z₂, z₃ are the vertices of an equilateral triangle

inscribed in the circle |z|=1 then the square of area of

quadrilateral z₁z₂z₃(-z₂) is

Answer: 3

naveen_nvn

in circle |z|=1, the three vertices r corresponding 2 cube roots of unity...i.e, a triangle wid sides of length root3..(cuz (0,1), (-root3/2,-0.5) and (root3/2,-0.5) r the three points)
so area of triangle is 0.5*root3*1.5 = 3*(root3)/4
now ur quadrilateral is twice the area of this triangle as u r just taking reflexion of Z2 about an axis so as 2 get this same triangle again
so required are shud b 3*(root 3)/2...
hope im rite...temme if wrong

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