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

Question

If $ \left|z^{2}-1\right|=|z|^{2}+1 $, then $ z $ lies on, the real axis, the imaginary axis, a circle, an ellipse

MARKS App · Accepted Answer

Using the relation, if z 1 + z 2 = z 1 + z 2 Then, arg z 1 = arg z 2 since, z 2 + - 1 = z 2 + - 1 Then, arg z 2 = arg - 1 ⇒ 2 arg z = π ∵ arg - 1 = π ⇒ arg z = π 2 ⇒ z lies on Y -axis (imaginary axis).

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