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line integral of a complex valued function by EASY MATHS EASY TRICKS

2,095 views · Published 4 March 2018 · 2:00 · Indexed 16 October 2026

Channel: EASY MATHS EASY TRICKS · 2018 · Education

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in this video explaining line integral of a complex valued function and this very simple method. A line integral is a type of integral where you integrate a function over a curve in a plane. If the function is complex valued, then the line integral is also complex valued.
Suppose we have a complex valued function f(z) and a curve C in the complex plane. The line integral of f(z) along C is denoted by ∫C f(z) dz and is defined as:
where a and b are the endpoints of the curve C t is a parameter that traces out the curve C as t ranges from a to b z(t) is the position vector of the curve C at time t and z'(t) is the derivative of z(t) with respect to t.
In other words the line integral of f(z) along C is the integral of f(z) evaluated at each point on the curve C weighted by the velocity of the curve at that point.
The line integral of a complex valued function along a closed curve is called a contour integral and is denoted by ∮C f(z) dz. Contour integrals have important applications in complex analysis especially in the study of complex functions and their properties.

#integral #complex 

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