question_answer

If\[|{{z}^{2}}-1|=|z{{|}^{2}}+1,\]then z lies on

A) the real axis

B) the imaginary axis

C) a circle

D) an ellipse

Correct Answer: B

Solution :

If complex number is the form of then Given that It shows that the origin. -1 andlies on a line and and - 1 lies on one side of the origin, thereforeis a negative number. Hence, z will be purely imaginary. So, we can say that z lies on y-axis. Alternate Solution We know that, if                                                             z lies on y-axis (imaginary axis).