Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Complex Number

NDA 2024 · Mathematics · Complex Number

If x, y and z are the cube roots of unity, then what is the value...

If x,yx, y and zz are the cube roots of unity, then what is the value of xy+yz+zxx y+y z+z x ?

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

A. 0

Step-by-step solution

∵x,y,z\because x, y, z are cube root of unity  Let, x=1,y=w,z=w2∴ Value of xy+yz+zx=1×w+w×w2+w2×1=w+w3+w2\begin{aligned} & \text{ Let, } x=1, y=w, z=w^2 \\ & \therefore \text{ Value of } x y+y z+z x \\ & =1 \times w+w \times w^2+w^2 \times 1 \\ & =w+w^3+w^2\end{aligned}\left[∵w3=11+w+w2=0\begin{array}{l}\because w^3=1 \\ 1+w+w^2=0\end{array}\right]=w+1+w2=1+w+w2=0\begin{aligned} & =w+1+w^2 \\ & =1+w+w^2=0\end{aligned}$
Practice Complex Number on Quantrex Academy →

More from Complex Number

Consider the following inequalities : I. 1+4i > 3+2i II. 2+3i III. 4+3i > 3+4i where i=… NDA 2026If p , q , r are the cube roots of unity, then what is vmatrix p^2+q^2 and r^2 and r^2… NDA 2026If α , β , γ are cube roots of -8 , then what is (α^2 p^2+β^2 q^2+γ^2 r^2)/(β^2 p^2+γ^2… NDA 2026Let Z_1 and Z_2 be complex numbers such that (3Z_1)/(4Z_2) is purely imaginary. What is… NDA 2026If ω is a non-real cube root of unity, then what is a root of the following equation?… NDA 2025If x + (1)/(x) = 2 θ , then what is x^3 + (1)/(x^3) equal to? NDA 2025If z ≠ 0 is a complex number, then what is amp(z) + amp( z ) equal to? NDA 2025If α = -1 + -3 2 , then what is the value of (1 + α^ 19 - α^ 35 )^ 100 - (1 - 3α^ 25 + α^… NDA 2025What is ( 3 +i 3 -i )^3 equal to? NDA 2025If ((1-i)/(1+i))^ 2m ((1+i)/(1-i))^ 2n = 1 , where i = -1 , then what is the smallest… NDA 2025Let 1 , ω , ω^2 be three cube roots of unity. If x = a + b , y = aω + bω^2 , z = aω^2 +… NDA 2025If ω ≠ 1 is a cube root of unity, then what is (1+ω-ω^2)^ 100 +(1-ω+ω^2)^ 100 equal to? NDA 2024What is the value of the sum ∑_ n=1 ^ 20 (i^ n-1 +i^n+i^ n+1 ) where i= -1 ? NDA 2024If ω=-(1)/(2)+i 3 2 then what is | array ccc 1+ω & 1+ω^2 & ω+ω^2 1 & ω & ω^2 (1)/(ω) &… NDA 2024What is (1+i)^4+(1-i)^4 equal to, where i= -1 ? NDA 2024If ω ≠ 1 is a cube root of unity, then what are the solution of (z-100)^3+1000=0 ? NDA 2024 Full Complex Number list Complex Number JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs