Prove that following inequalities:
(i) `|(z)/(|z|) -1| le |arg z|` (ii) `|z-1|le|z| |arg z | + |z|-1|`

Explanation

To prove the given inequalities, we will work through each part step by step.

### Part (i): Prove that \( \left| \frac{z}{|z|} - 1 \right| \leq |\arg z| \)

1. **Express \( z \) in polar form**:
Let \( z = |z|(\cos \theta + i \sin \theta) \), where \( \theta = \arg z \).

2. **Substitute \( z \) into the left-hand side (LHS)**:
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