If `z=x+i y` and `w=(1-i z)/(z-i)` , show that `|w|=1 z` is purely real.

Explanation

To solve the problem, we need to show that if \( |w| = 1 \), then \( z \) is purely real. We start with the definitions given in the problem:

1. Let \( z = x + iy \).
2. Let \( w = \frac{1 - iz}{z - i} \).

We need to find \( |w| \) and show that if \( |w| = 1 \), then \( y = 0 \) (which means \( z \) is purely real).

### Step-by-Step Solution:
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