Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202423 May 2024Morning ShiftMathematicsComplex NumberActual

If the roots of the equation Z^3+i Z^2+2 i=0 are the vertices of a triangle A B C . then that triangle A B C is

Options

  1. Aa right angled triangle
  2. Ban equilateral triangle
  3. Can isosceles triangle
  4. Da right angled isosceles triangle

Correct answer

C. an isosceles triangle

Step-by-step solution

Given, Z^3+i Z^2+2 i=0 aligned & (Z-i) (Z^2+2 i Z-2 )=0 & Z=i or Z^2+2 i Z-2=0 & Z= -2 i 2 2 z=-i+1,-i-1 aligned Let A(0,1), B(1,-1), C(-1,-1)A B= 5 ; B C=2 ; A C= 5 Since, A B^2+A C^2 B C^2 and A B=B C B C . So, A B C is an isosceles triangle.

Practice Complex Number on Quantrex Academy →

More from Complex Number

If z and are two non-zero complex numbers such that |z |=1 and Arg z- Arg = 2 then z = 2025Let z satisfy |z|=1, z=1- z and Im (z)>0 Statement-I : z is a real number Statement-II : Principal argument of z is 3 . Then 2025If ₁ and ₂ are two non-zero complex numbers and a , b are non zero real numbers such that | a ₁+ b ₂ |= | a ₁- b ₂ | , then ₁ ₂ is 2025If a complex number z=x+i y represents a point P on the Argand plane and Arg ( z-3+2 i z+2-3 i )= 4 , then the locus of P is a 2025By taking a i b =x i y, x>0 , if we get 21+12 2 i 21-12 2 i =a+i b , then b a = 2025Two values of (-8-8 3 i)^ 1 / 4 are 2025If x=3-2 3 i , then x^4-12 x^3+54 x^2-108 x-54= 2025z ₁, z ₂, z ₃ represent the vertices A , B , C of a triangle ABC respectively in the Argand plane. If |z₁-z₂ |= 25-12 3 , | z₁-z₃ z₂-z₃ |= 3 4 and ACB =30^ , then the area (in sq. 2025 Full Complex Number list All AP EAMCET PYQs