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If omega = z//[z-(1//3)i] and |omega| = ...

If `omega = z//[z-(1//3)i] and |omega| = 1`, then find the locus of z.

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The correct Answer is:
Perpendicular bisector of the line joininig 0+ 0i and `0 + (1//3)i`
`omega = (z)/(z-(1)/(2)i)`
or ` |omega| = |(z)/(z-(1)/(3)i)|`
or ` |z| = |omega||z-(1)/(3)i|`
or ` |z| = |z-(1)/(3)i|" "(because |omega|=1)`
Hence, locous of z is perpendicular bisector of the line joining `0 + 0i` and `0+(1//3)i`. Hence z lies on a straight line .
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