Complex NumbersHard
Question
Let A, B, C represent the complex numbers z1, z2, z3 respectively on the complex plane. If the circumcentre of the triangle ABC lies at the origin, then the orthocentre is represented by the complex number :
Options
A.z1 + z2 - z3
B.z2 + z3 - z1
C.z3 + z1 - z2
D.z1 + z2 + z3
Solution
G → Centroid of ᐃ = 
H → Orthocentre = z say, O → Circum centre = 0
∵ G divides HO in ratio 2 : 1 reckening from
⇒ z = z1 + z2 + z3
H → Orthocentre = z say, O → Circum centre = 0
∵ G divides HO in ratio 2 : 1 reckening from
⇒ z = z1 + z2 + z3 Create a free account to view solution
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