If (z3-z1/z3-z2)=i, then points z1, z2 and z3

Question

If (z3-z1/z3-z2)=i, then points z1, z2 and z3 (A) are collinear (B) forms equilateral triangle (C) forms isosceles right angled triangle (D) forms obtuse angled triangle

Tardigrade Admin · Accepted Answer

(z3-z1/z3-z2)=i ∴ |(z3-z1/z3-z2)|=1 ∴ |z3-z1|=|z3-z2| Also arg ((z3-z1/z3-z2))=(π/2) ∴ angle at vertex z3 is 90° Hence triangle is isosceles right angled.

Q. If z3​−z2​z3​−z1​​=i, then points z1​,z2​ and z3​

are collinear

forms equilateral triangle

forms isosceles right angled triangle

forms obtuse angled triangle

z3​−z2​z3​−z1​​=i ∴∣∣​z3​−z2​z3​−z1​​∣∣​=1 ∴∣z3​−z1​∣=∣z3​−z2​∣ Also arg(z3​−z2​z3​−z1​​)=2π​ ∴ angle at vertex z3​ is 90∘ Hence triangle is isosceles right angled.

Q. If $\frac{z _{3} - z _{1}}{z _{3} - z _{2}} = i$ , then points $z_{1}, z_{2}$ and $z_{3}$