If `z` is a complex number such that `|z|=1,` prove that `(z-1)/(z+1)` is purely imaginary, what will by your conclusion if `z=1?`

Explanation

To prove that \(\frac{z-1}{z+1}\) is purely imaginary when \(|z| = 1\), we can follow these steps:

### Step 1: Express \(z\) in terms of its real and imaginary parts
Let \(z = x + iy\), where \(x\) and \(y\) are real numbers. Given that \(|z| = 1\), we have:
\[ |z| = \sqrt{x^2 + y^2} = 1 \]
Squaring both sides gives:
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