Complex line integral

•

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𝐶
𝑑𝑧
𝑧 − 1
=
0
2𝜋
1
𝑒 𝑖𝜃
⋅ 𝑖𝑒 𝑖𝜃
𝑑𝜃 = 𝑖
0
2𝜋
𝑑𝜃 = 2𝜋𝑖
𝐶: 𝑧 = 1 ⇔ 𝑧 = 1 + 𝑒 𝑖𝜃 (0 ≤ 𝜃 < 2𝜋)
𝑑𝑧
𝑑𝜃
= 𝑖𝑒 𝑖𝜃 ∴ 𝑑𝑧 = 𝑖𝑒 𝑖𝜃 𝑑𝜃
2015/04/29 Hanpen Robot

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Complex line integral

1. 𝐶 𝑑𝑧 𝑧 − 1 = 0 2𝜋 1 𝑒 𝑖𝜃 ⋅ 𝑖𝑒 𝑖𝜃 𝑑𝜃 = 𝑖 0 2𝜋 𝑑𝜃 = 2𝜋𝑖 𝐶: 𝑧 = 1 ⇔ 𝑧 = 1 + 𝑒 𝑖𝜃 (0 ≤ 𝜃 < 2𝜋) 𝑑𝑧 𝑑𝜃 = 𝑖𝑒 𝑖𝜃 ∴ 𝑑𝑧 = 𝑖𝑒 𝑖𝜃 𝑑𝜃 2015/04/29 Hanpen Robot