The curve represented by $R e (z^{2}) = 4$ is

a parabola

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an ellipse

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a circle

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a rectangular hyperbola

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Solution

The correct option is D a rectangular hyperbola
Let
$z = x + i y$
Hence
$z^{2} = x^{2} - y^{2} + i 2 x y$
Now
$R e (z^{2})$
$= x^{2} - y^{2}$
$= 4$
Hence
$x^{2} - y^{2} = 4$
Represents a hyperbola.

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