Step-by-Step Solution
Key Concept: For $\arg(z)\in(-\pi,0)$, adding $\pi$ lands in $(0,\pi)$, still within the principal range, so $\arg(-z)=\arg(z)+\pi$ exactly and the difference is $\pi$.
**Step 1: Establish the range**
Given $\arg(z) < 0$, so $\arg(z) \in (-\pi, 0)$ (principal argument).
**Step 2: Find arg(−z)**
Multiplying by $-1 = e^{i\pi}$ adds $\pi$: $\arg(-z) = \arg(z)+\pi \in (0,\pi) \subset (-\pi,\pi]$. No wrap-around adjustment needed.
**Step 3: Compute the difference**
$\arg(-z)-\arg(z) = (\arg(z)+\pi)-\arg(z) = \pi$.
Correct Answer: 1