The locus of a point in the Argand plane that moves satisfying the equation, $| z - 1 + i | - | z - 2 - i | = 3$

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is none of hte above.

is an ellipse with its foci at 1 – i and 2 + i and major axis = 3

is a circle with radius 3 & centre at $z = 3 / 2$

is a hyperbola with its foci at 1– i and 2 + i and its transverse axis = 3

answer is B.

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Detailed Solution

$\begin{array}{l} | z - (1 - i) | - | z - (2 + i) | = 3 \\ z_{1} = 1 - i = (1, - 1); 2 a = 3; z_{2} = 2 + i = (2, 1) \\ \Rightarrow |z_{1} - z_{2}| = \sqrt{5} < 3; {ss}^{1} < 2 a \Rightarrow So no locus \end{array}$

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