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  4. In a complex plane, the point z moves such that |z-3i|=2 then its locus is

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Q. In a complex plane, the point $z$ moves such that $ |z-3i|=2 $ then its locus is

Rajasthan PETRajasthan PET 2004

Solution:

$ |z-3i|=2 $
$ \Rightarrow $ $ |x+iy-3i|=2 $
$ \Rightarrow $ $ |x(y-3)i|=2 $
$ \Rightarrow $ $ \sqrt{{{x}^{2}}+{{(y-3)}^{2}}}=2 $
$ \Rightarrow $ $ {{x}^{2}}+{{(y-3)}^{2}}=4; $
which represents a circle.