If a triangle ABC is formed by the points represented by z,iz and z+iz then
A
ABC is an equilateral triangle
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B
ABC is an isosceles right angled triangle
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C
Area of △ABC is 12|z|2 sq. units
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D
Area of △ABC is √34|z|2 sq. units
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Solution
The correct options are BABC is an isosceles right angled triangle C Area of △ABC is 12|z|2 sq. units
Let A(z),B(iz),C(z+iz) be vertices of ΔABC Then CA=|z+iz−z|=|iz|=|z| CB=|z+iz−iz|=|z| AB2=|z−iz|2=|z|2+|iz|2−2Re(z⋅¯¯¯¯¯iz) =|z|2+|z|2−2Re(−i|z|2) =2|z|2−0 =2|z|2=CA2+CB2 ∴ABC is right angled isosceles triangle. Area of △ABC=12CA×CB =12|z|2