# If  and ,then  lies on

Therefore

$\\\left | \frac{z}{z-(1/3)i} \right |=1\\ |z|=|z-(1/3)i|$

Let z = a + ib

$\\|z|=|z-(1/3)i|\\ \sqrt{a^{2}+b^{2}}=\sqrt{a^{2}+(b-1/3)^{2}}\\ a^{2}+b^{2}=a^{2}+b^{2}-\frac{2b}{3}+\frac{1}{9}\\ b=\frac{1}{6}$

$a\epsilon \mathbb{R}$

z lies on the line$y=\frac{1}{6}$

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