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
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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 $z_2 = z+3i$.