AP EAMCET201824 Apr 2018Morning ShiftMathematicsComplex NumberActual
If Z 1 is a complex number and Arg ( Z-1 Z+1 )= 4 , then the locus of Z in the Arg and plane is
Options
- Ax^2+y^2-2 y-1=0
- Bx^2+y^2+2 y-1=0
- Cx^2+y^2-2 x+1=0
- Dx^2+y^2+2 x+1=0
Correct answer
A. x^2+y^2-2 y-1=0
Step-by-step solution
aligned & Let z=x+i y & aligned z-1 z+1 & = x+i y-1 x+i y+1 & = (x-1)+i y (x+1)+i y (x+1)-i y (x+1)-i y & = x^2+y^2-1+2 i y (x+1)^2+y^2 ( z-1 z+1 ) & = ⁻¹ ( 2 y x^2+y^2-1 ) & = / 4 & 2 y x^2+y^2-1 = / 4=1 x^2+y^2-1=2 y & x^2-2 y-1=0 . aligned aligned