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AP EAMCET202422 May 2024Evening ShiftMathematicsComplex NumberActual

If P (x, y) represents the complex number z=x+i y in the Argand plane and Arg ( z-3 i z+4 )= 2 , then the equation of the locus of P is

Options

  1. Ax^2+y^2+4 x-3 y=0 and 3 x-4 y 0
  2. Bx^2+y^2+4 x-3 y+2=0 and 3 x-4 y 0
  3. Cx^2+y^2+4 x-3 y=0 and 3 x-4 y 0
  4. Dx^2+y^2+4 x-3 y+2=0 and 3 x-4 y 0

Correct answer

C. x^2+y^2+4 x-3 y=0 and 3 x-4 y 0

Step-by-step solution

aligned & z-3 i z+4 = x+(y-3) i (x+4)+y i (x+4)-y i (x+4)-y i &= x(x+4)-x y i+(x+4)(y-3) i+y(y-3) (x+4)^2+y^2 &= x^2+y^2+4 x-3 y+(4 x-3 x) i (x+4)^2+y^2 & Arg ( z-3 i z+4 )= 2 2 = 4 y-3 x x^2+y^2+4 x-3 y & x^2+y^2+4 x-3 y=0 aligned Also, for I ^ st quadrant, 4 y-3 x 0 3 x-4 y 0

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