lf $Z = 3 + 2 i$ then

$(Z + ¯ ¯¯ ¯ Z)^{2} + (Z - ¯ ¯¯ ¯ Z)^{2} - 3 Z ¯ ¯¯ ¯ Z =$

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-19

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Solution

The correct option is B -19
$z + ¯ z = 2 R e (z) = 2 \times 3 = 6$
$z - ¯ z = 2 i I m (z) = 4 i$
$z ¯ z = {| z |}^{2} = (\sqrt{3^{2} + 2^{2}})^{2} = 13$
$\Rightarrow (z + ¯ z)^{2} + (z - ¯ z)^{2} - 3 z ¯ z$
$= 36 - 16 - 3 * 13$
$= - 19$

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