If - z 2-1- z -2-1- then z lies onA- the real axisB- an ellipseC- a circleD- the imaginary axis

The correct option is D the imaginary axisGiven that |z^2 1|=|z^2|+1 ⇒ |z^2+( 1)|=|z^2|+| 1| It shows that the origin, 1, and z^2 lie on a line and z^2 and 1 ...

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Standard XII

Mathematics

Modulus of a Complex Number

If | z 2-1|=|...

Question

If $| z^{2} - 1 | = | z |^{2} + 1$ , then z lies on

the real axis

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an ellipse

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a circle

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the imaginary axis

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Solution

The correct option is D the imaginary axis
Given that
$| z^{2} - 1 | = | z^{2} | + 1 \Rightarrow | z^{2} + (- 1) | = | z^{2} | + | - 1 |$
It shows that the origin, -1, and $z^{2}$ lie on a line and $z^{2}$ and -1 lie on one side of the origin. Therefore, $z^{2}$ is a negative number. Hence, z will be purely imaginary. So we can say that z lies on the y-axis.

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If |z2−1|=|z|2+1, then z lies on

If $| z^{2} - 1 | = | z |^{2} + 1$ , then z lies on