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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