Question:medium

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

Show Hint

A number is purely real if its imaginary part is zero. For a complex fraction $\frac{z_1}{z_2}$, a quick way to find the condition for it to be purely real is to set $\text{Im}(z_1\bar{z_2}) = 0$. In this case, $z_1 = z-3$ and $z_2 = z+3i$.
Updated On: Mar 30, 2026
  • $x^2+y^2-3x+3y= 0, (x, y) \neq (0,-3)$
  • $2xy-3x+3y+9=0, (x, y) \neq (0,-3)$
  • $x-y-3=0, (x, y) \neq (0,-3)$
  • $x+y+3=0, (x, y) \neq (0,-3)$
Show Solution

The Correct Option is C

Solution and Explanation

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