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    Finding the locus of all points in the complex plane.

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    Please give details of soln

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

    © BrainMass Inc. brainmass.com March 4, 2021, 7:18 pm ad1c9bdddf
    https://brainmass.com/math/complex-analysis/finding-locus-points-complex-plane-93172

    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.,
    ...

    Solution Summary

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

    $2.49

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