Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Complex Number

NDA 2023 · Mathematics · Complex Number

If z z =|z+ z | , where z=x+i y, i= -1 then the locus of z is a...

If zzˉ=∣z+zˉ∣z \bar{z}=|z+\bar{z}|, where z=x+iy,i=−1z=x+i y, i=\sqrt{-1} then the locus of zz is a pair of :

Options

  1. AStraight lines
  2. Brectangular hyperbolas
  3. Cparabolas
  4. Dcircles

Correct answer

D. circles

Step-by-step solution

 Since, z=x+iy Now, (x+iy)(x−iy)=∣x+iy+x−iy∣⇒x2−(iy)2=∣2x∣⇒x2+y2=2x⇒x2−2x+1+y2=1⇒(x−1)2+y2=1\begin{aligned} & \text{ Since, } \mathrm{z}=\mathrm{x}+\mathrm{iy} \\ & \text{ Now, }(\mathrm{x}+\mathrm{iy})(\mathrm{x}-\mathrm{iy})=|\mathrm{x}+\mathrm{iy}+\mathrm{x}-\mathrm{iy}| \\ \Rightarrow & \mathrm{x}^2-(\mathrm{iy})^2=|2 \mathrm{x}| \\ \Rightarrow & \mathrm{x}^2+\mathrm{y}^2=2 \mathrm{x} \Rightarrow \mathrm{x}^2-2 \mathrm{x}+1+\mathrm{y}^2=1 \\ \Rightarrow & (\mathrm{x}-1)^2+\mathrm{y}^2=1 \end{aligned} So locus of zz is circle
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