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Question

If $$Rez^2=0$$ then the locus of z is


A
Circle
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B
Parabola
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C
Pair of non-perpendicular lines
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D
Pair of perpendicular lines
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Solution

The correct option is D Pair of perpendicular lines
Let,
$$z=x+iy$$
$$z^{2}=x^{2}+2ixy-y^{2}$$
$$Re\left ( z^{2} \right )=0$$
$$\Rightarrow x^{2}-y^{2}=0$$
$$\Rightarrow \left ( x+y \right )\left ( x-y \right )=0$$
$$\Rightarrow x+y=0     \ or\    x-y=0$$
Hence, option D is correct

Maths

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