[複變]路徑積分問題
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f(z)= z dz 積分路徑為-2i到2i，一、四象限的右半圓，半徑為2
用e=e^iθ 得到積分結果是4πi
再取另一個路徑y軸上y=2到y=-2
用 z=x+iy帶入 直接積y軸上路徑會得到結果是 0
兩個結果相加是4πi
可是根據柯西-高賽定理 一個函數在封閉的contour裡是完全可以解析的
那麼積分結果會是0
可是根據我上面的算法卻不是0
請問是錯在哪裡？
感謝解答
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