1.

If `|z-5i|=|z+5i`, then the locus of `zdot`

Answer» Let `z = x+iy`
Then,
`|x+iy-5i| = |x+iy+5i|`
`=>|x+(y-5)i| = |x+(y+5)i|`
`=>x^2+(y-5)^2 = x^2+(y+5)^2`
`=> -10y = 10y`
`=> -20y = 0`
`=> y = 0`
So, imaginary part of `z` is `0`.
We can write it as,
`(z-barz)/2 = 0`
`z - barz = 0`, which is the required locus.


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