Suppose A(z 1 ), B(z 2 ) and C(z 3 ) are vertices of a triangle lying on the unit circle…
Mathematics · JEE Advanced · NTA Exams — Complex Numbers and Quadratic Equations
Suppose A(z1), B(z2) and C(z3) are vertices of a triangle lying on the unit circle |z| = 1. AD is altitude of the ∆ABC meeting the unit circle in E.
- orthocentre of ∆ABC is z1 + z2 + z3
- affix of E is –z2z3/z1
- if z12 = z2z3 and z22 = z3z1, then ∆ABC is equilateral
- if z2 + z3 = 0, then ∆ABC is a right angled.
Answer
(A) orthocentre of ∆ ABC is z 1 + z 2 + z 3, (B) affix of E is –z 2 z 3 /z 1, (C) if z 1 2 = z 2 z 3 and z 2 2 = z 3 z 1 , then ∆ ABC is equilateral, (D) if z 2 + z 3 = 0, then ∆ ABC is a right angled.
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