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The problem provided is asking to calculate the complex line integral:

\[
\int_C |z| \, dz
\]
where \( C \) is the upper half of the circle with radius 2, connecting \(-2\) to \(2\).

### Interpretation:
1. The integral is over a semicircular path \( C \) on the complex plane, specifically the upper half of the circle \( |z| = 2 \), from \( z = -2 \) to \( z = 2 \).
2. The function being integrated is \( |z| \), which represents the modulus of \( z \) (the distance of \( z \) from the origin).

### Solution outline:
1. **Parameterization of the curve**: Since \( C \) is the upper half of the circle \( |z| = 2 \), we can parametrize it using:
   \[
   z(\theta) = 2e^{i\theta}, \quad \theta \in [\pi, 0]
   \]
   where \( \theta = \pi \) corresponds to \( z = -2 \) and \( \theta = 0 \) corresponds to \( z = 2 \).

2. **Modulus of \( z \)**: For any \( z \) on this circle, \(

计算 ∫_C |z| dz, C为连接-2到2的上半圆。

Learn how to solve the complex line integral ∫_C |z| dz where C is the upper half-circle connecting -2 to 2. This detailed guide covers the key concepts of parametrization in complex analysis and evaluates the integral step by step.

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