1.

If z is a complex number satisfying |z|^(2)+2(z+2)+3i(z-barz)+4 =0, then complex number z+3+2i lies on

Answer»

circle witih center 1-5i and radius 4
circle with center 1+5i and radius 4
circle with center 1+5i and radius 3
circle with center 1-5i and radius 3

Solution :We have,
`|z|^(2)+2(z+barz)+3i(z-barz)+4=0`
`RARR zbarz+(2+3i)z+(2-3i)barz+4=0`
CLEARLY, it REPRESENTS a circle with centers as `(-2,3)` and radius `=sqrt(4+9-4)=3`.
The above equation can be written as
`|z-(2+3i)|=4` or , `|z+2-3i|=4 rArr |omega-3-2i+2-3i|=4 rArr |omega-1-5i|=4`
`rArr omega` lies on the circle with center 1+5i and radius 4.


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