Find the minimum value of `|z-1|` if `||z-3|-|z+1||=2.`

Explanation

To find the minimum value of \( |z - 1| \) given that \( ||z - 3| - |z + 1|| = 2 \), we can follow these steps:

### Step 1: Understanding the Given Condition
We start with the equation:
\[ ||z - 3| - |z + 1|| = 2 \]
This means that the difference between the distances from the point \( z \) to the points \( 3 \) and \( -1 \) is equal to \( 2 \).
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