If a complex number $z=x+i y$ represents a point $\mathrm{P}(x, y)$ in the Argand plane and $z$ satisfies the condition that the imaginary part of $\frac{z-3}{z+3 i}$ is zero, then the locus of the point P is

• A

  $x^2+y^2-3 x+3 y=0,(x, y) \neq(0,-3)$
• B

  $2 x y-3 x+3 y+9=0,(x, y) \neq(0,-3)$
• Correct answer
  C

  $x-y-3=0,(x, y) \neq(0,-3)$
• D

  $x+y+3=0,(x, y) \neq(0,-3)$

Hence, the correct answer is option: 'C'.