If three complex numbers z1,z2 and z3 satisfy z1−z3z2−z3=1−i√32, then the triangle formed by z1,z2 and z3 is
A
scalene
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B
right-angled isosceles
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C
equilateral
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D
obtuse-angled isosceles
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Solution
The correct option is C equilateral z1−z3z2−z3=1−i√32⇒z1−z3z2−z3=e−iπ/3⋯(1)
Now using the rotation concept we get z1−z3z2−z3=|z1−z3||z2−z3|e−iπ/3⋯(2) comparing (1) and (2), we get |z1−z3|=|z2−z3| and angle between any two sides is 60° Hence the given triangle is equilateral triangle.