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If w=z/[z-(1/3)i] and |w|=1, then find ...

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

Text Solution

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`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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