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
View Solution FreeMore Complex Numbers Questions
If w is an imaginary cube root of unity, then for positive integral value of n, the product of ω. ω2.ω3.....If z = x + iy and z1/3 = a - ib then = k(a2 - b2) where k =...If z1, z2, z3, z4 are any four points in a complex plane and z is a point such that |z − z1| = |z − z2| = |z...If z1 = , a ≠ 0 and z2 = , b ≠ 0 are such that z1 = then -...The set of points on an Arg and diagram which satisfy both | z | ≤ 4 & Arg z = π/3 are lying on -...