# Complex numbers again

Algebra Level 4

If $$z$$ be a complex number satisfying$${ |z| }^{ 2 }+2(z+\overline { z } )+3i(z-\overline { z } )+4=0$$, then complex number $$z+3+2i$$ will lie on a circle with centre $$a+bi$$ and radius $$c$$ units.

Find $$|a+b+c|$$.

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