If z is a complex number satisfying |z|2+2(z+z¯)+3i(z−z¯)+4=0,i=−1,then the complex number z + 3 + 2i will lie on a circle with

Given |z+(2−3i)|=3Let w = (z+3+2i)=z+2−3i+1+5iw-1+5i=z+2-3i⇒|w−(1+5i)|=|z+2−3i| ⇒|w−(1+5i)|=3

If z is a complex number satisfying |z|2+2(z+z¯)+3i(z−z¯)+4=0,i=−1,then the complex number z + 3 + 2i will lie on a circle with

Given |z+(2−3i)|=3Let w = (z+3+2i)=z+2−3i+1+5iw-1+5i=z+2-3i⇒|w−(1+5i)|=|z+2−3i| ⇒|w−(1+5i)|=3

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If z is a complex number satisfying $| z |^{2} + 2 (z + \bar{z}) + 3 i (z - \bar{z}) + 4 = 0, i = \sqrt{- 1},$ then the complex number z + 3 + 2i will lie on a circle with

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centre 1–5i, radius 4

centre 1+ 5i, radius 3

centre 1–5i, radius 3

answer is C.

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Given $| z + (2 - 3 i) | = 3$
Let w = $(z + 3 + 2 i) = z + 2 - 3 i + 1 + 5 i$

$w - (1 + 5 i) = z + 2 - 3 i$
$\Rightarrow | w - (1 + 5 i) | = | z + 2 - 3 i | \Rightarrow | w - (1 + 5 i) | = 3$

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If z is a complex number satisfying |z|2+2(z+z¯)+3i(z−z¯)+4=0,i=−1,then the complex number z + 3 + 2i will lie on a circle with

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If z is a complex number satisfying $| z |^{2} + 2 (z + \bar{z}) + 3 i (z - \bar{z}) + 4 = 0, i = \sqrt{- 1},$ then the complex number z + 3 + 2i will lie on a circle with