If $| z + 3 + 2 i | = | z + 2 + 3 i |$ , then the locus of $z$ is:

A straight line

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Circle

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Parabola

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Hyperbola

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Solution

The correct option is B A straight line
$| z - (- 3 - 2 i) = | z - (- 2 - 3 i) |$
$\Rightarrow$ distance of $z$ from A $(- 3, - 2)$ is same as
that from $B (- 2, - 3)$
$\Rightarrow$ z lies on the perpendicular bisector of $A B$

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