Visualizing Complex Line Integral

[et_pb_section fb_built="1" _builder_version="3.0.47"][et_pb_row _builder_version="3.0.47" background_size="initial" background_position="top_left" background_repeat="repeat"][et_pb_column type="4_4" _builder_version="3.0.106" parallax="off" parallax_method="on"][et_pb_text _builder_version="3.0.106" custom_padding="|20px||20px" box_shadow_style="preset1"] There is nothing complex about complex line integral. It is just vector addition (and taking a limit of that sum). Let's take a concrete example: $$\oint_{\lambda} \frac {1}{\zeta} d \zeta = 2 \pi i$$ Here, let $\lambda$ be the unit circle centered at the origin. Then we pick $\zeta$ from the circumference of the circle. Suppose we work with polar coordinates. Then the coordinate of a typical $\zeta$ is $(1, \theta)$.

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