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 amp (zi) = θi, i = 1, 2, 3; then amp is equal to-...If g(x) and h(x) are two polynomials such that the polynomial P(x) = g(x3) + xh(x3) is divisible by x2 + x + 1, then -...If ω is one imaginary nth root of unity, then the value of 1 + ω + ω2 + ..... + ωn−1 is-...In G.P. the first term & common ratio are both (√3 + i), then the absolute value of its nth term is :...The roots of the cubic equation (z + ab)3 = a3, a ≠ 0 represents the vertices of an equilateral triangle of sides ...