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Geometrical Representation of a Complex Number

If z = x + iy...

Question

If $z = x + i y$ and $R e (z^{2}) = 0$ , then the locus of $z$ can be

A

y = x

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B

y = - x

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C

y = 2 x

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D

y = - 2 x

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Solution

The correct options are
A $y = x$
B $y = - x$
$z = x + i y \Rightarrow z^{2} = x^{2} - y^{2} + 2 i x y$
Now,
$R e (z^{2}) = 0 \Rightarrow x^{2} - y^{2} = 0 \Rightarrow y = x or y = - x$

Hence, the required locus are $y = x$ or $y = - x$

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Geometrical Representation of a Complex Number

Standard XII Mathematics

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