Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201822 Apr 2018Morning ShiftMathematicsComplex NumberActual

If 1, , ^2 are the cube roots of unity, then 1 1+2 + 1 2+ - 1 1+ =

Options

  1. A1
  2. B^2
  3. C0

Correct answer

3

Step-by-step solution

aligned & Given, 1 1+2 + 1 2+ - 1 1+ & = 2+ +1+2 (1+2 )(2+ ) - 1 (1+ ) & = 3+3 (1+2 )(2+ ) - 1 (1+ ) & = (3+3 )(1+ )-(1+2 )(2+ ) (1+2 )(2+ )(1+ ) & = 3+3 +3 +3 ^2- (2+ +4 +2 ^2 ) (1+2 )(2+ )(1+ ) & = 3+6 +3 ^2-2-w-4 -2 ^2 (1+2 )(2+ )(1+ ) & = 1+ + ^2 (1+2 )(2+ )(1+ ) & =0 aligned

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