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Question

If |z21|=|z|2+1, then z lies on

A
the real axis
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B
an ellipse
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C
a circle
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D
the imaginary axis
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Solution

The correct option is D the imaginary axis
Given that
|z21|=|z2|+1|z2+(1)|=|z2|+|1|
It shows that the origin, -1, and z2 lie on a line and z2 and -1 lie on one side of the origin. Therefore, z2 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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