Complex Line Integrals and the Fundamental Theorem of Calculus

In the previous video 'Integrating Complex Valued Functions of a Real Variable' at • Integrating Complex Va... we tackled various questions where we were asked to integrate a complex-valued function of a real variable along the real axis only. In this video we expand on that to discuss integrating complex valued functions of a complex variable along various paths in the complex plane.
As we shall see in the examples we discuss in this video, because the complex functions we integrate are holomorphic (complex differentiable), we can again use the Fundamental Theorem of Calculus, though we also show how to integrate along various complex paths.
Some may find the video 'Fundamental Theorem of Calculus for Line Integrals of Conservative Vector Fields F(x,y,z)' at • Fundamental Theorem of... useful, because the discussions are very similar to those in this video.
For more practice with complex numbers see our playlist 'Complex Numbers' at • Complex Numbers

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For more on calculus of complex numbers see our playlist 'Calculus of Complex Numbers' at th-cam.com/play/PLlX3COjsHPVC3950F2WhgxDR0-nyloONJ.html