If `|z^2-1|=|z|^2+1` , then show that `z` lies on the imaginary axis.

Explanation

To solve the problem, we need to show that if \( |z^2 - 1| = |z|^2 + 1 \), then \( z \) lies on the imaginary axis. We will represent \( z \) as a complex number in the form \( z = x + iy \), where \( x \) is the real part and \( y \) is the imaginary part.

### Step-by-Step Solution:

1. **Express \( z \) in terms of its components**:
\[ z = x + iy \]
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