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Find the locus of point z if z , i ,and ...

Find the locus of point `z` if `z` , `i` ,and `iz` , are collinear.

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Given that points z, i and iz are colliner.
`therefore arg ((z-i)/(iz -i)) = 0, pi`
So,`(z-i)/(iz -i) `is purely real.
`rArr (z-i)/(iz -i) = (vbarz +i)/(-ibarz +i)`
`rArr (z-1)/(z-1) = (barz +i)/(-ibarz + 1)`
`rArr 2zbarz + iz - ibarz- barz - z = 0`
`2(x^(2) +y^(2))-2x -2y =0`
`rArr x^(2) + y^(2) - x-y =0`
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