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Question

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
B ABC 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+izz|=|iz|=|z|
CB=|z+iziz|=|z|
AB2=|ziz|2=|z|2+|iz|22Re(z¯¯¯¯¯iz)
=|z|2+|z|22Re(i|z|2)
=2|z|20
=2|z|2=CA2+CB2
ABC is right angled isosceles triangle.
Area of ABC=12CA×CB
=12|z|2

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