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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 |
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Answer» circle witih center 1-5i and radius 4 `|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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