Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2006MathematicsComplex Number

The equation of the locus of z such that | z-i z+i |=2 , where z=x+i y is a complex number, is

Options

  1. A3 x^2+3 y^2+10 y-3=0
  2. B3 x^2+3 y^2+10 y+3=0
  3. C3 x^2-3 y^2-10 y-3=0
  4. Dx^2+y^2-5 y+3=0

Correct answer

B. 3 x^2+3 y^2+10 y+3=0

Step-by-step solution

| z-i z+i |=2 z=x+i y | x+i y-i x+i y+i |=2 | x+(y-1) i x+(y+1) i |=2 |x+i(y-1)|=2|x+(y+1) i| x^2+(y-1)^2=4 (x^2+(y+1)^2 ) x^2+y^2-2 y+1=4 y^2+8 y+4+4 x^2 3 x^2+3 y^2+10 y+3=0

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