# Finding the locus of all points in the complex plane.

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Please give details of soln

|z-i| + |z| = 9.

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#### Solution Preview

Solution. As |z-i| + |z| = 9 and let z = x + yi, then we have

|x+(y-1)i| + |x+iy|=9

So, |x+(y-1)i|=9-|x+iy|

So, squaring it, we have

|x+(y-1)i|^2=[9-|x+iy| ]^2=81-18|x+iy|+|x+iy|^2

i.e.,

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#### Solution Summary

Finding the locus of all points in the complex plane is investigated. The solution is detailed and well presented.

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