The points representing the complex numbers z for which $| z + 4 |^{2} - | z - 4 |^{2} = 8$ lie on

a straight line parallel to x-axis

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a straight line parallel to y-axis

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a circle with centre as origin

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a circle with centre other than the origin

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Solution

The correct option is B a straight line parallel to y-axis
Let $z = x + i y$ . Then,
$| z + 4 |^{2} - | z - 4 |^{2} = 8 \Rightarrow 4 R e (4 z) = 8$
$\Rightarrow R e (z) = \frac{1}{2}$
$\Rightarrow x = 1 / 2,$ which is a straight line parallel to y-axis.

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The points representing the complex numbers z for which |z+4|2−|z−4|2=8 lie on

The correct option is B a straight line parallel to y-axisLet z=x+iy. Then,|z+4|2−|z−4|2=8⇒4Re(4z)=8⇒Re(z)=12⇒x=1/2, which is a straight line parallel to y-axis.

The points representing the complex numbers z for which $| z + 4 |^{2} - | z - 4 |^{2} = 8$ lie on

The correct option is B a straight line parallel to y-axis
Let $z = x + i y$ . Then,
$| z + 4 |^{2} - | z - 4 |^{2} = 8 \Rightarrow 4 R e (4 z) = 8$
$\Rightarrow R e (z) = \frac{1}{2}$
$\Rightarrow x = 1 / 2,$ which is a straight line parallel to y-axis.