Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Complex Number

NDA 2021 · Mathematics · Complex Number

Consider the following statements in respect of an arbitrary...

Consider the following statements in respect of an arbitrary complex number ZZ : 1. The difference of ZZ and its conjugate is an imaginary number. 2. The sum of ZZ and its conjugate is a real number. Which of the above statements is/are correct?

Options

  1. A11 only
  2. B22 only
  3. CBoth 11 and 22
  4. DNeither 11 nor 22

Correct answer

C. Both 11 and 22

Step-by-step solution

Let z=x+iyz=x+i y conjugate of z′=x−iyz^{\prime}=x-i y Now, z+z′=x+iy+x−iy=2xz+z^{\prime}=x+i y+x-i y=2 x (Real) z−z′=x+iy−x+iy=(2y)iz-z^{\prime}=x+i y-x+i y=(2 y) i \quad (Imaginery) Hence, both (1) and (2) are true.
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 2024If x, y and z are the cube roots of unity, then what is the value of x y+y z+z x ? NDA 2024What is (1+i)^4+(1-i)^4 equal to, where i= -1 ? NDA 2024 Full Complex Number list Complex Number JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs