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Thread: Complex analysis

  1. #1
    Kai is offline
    Junior Member
    Apr 2008

    Complex analysis

    Find the length of the path gamma where

    gamma(t) = e^(-1+2it) , -2<=t<=2

    I missed 2 lecture class, and have no clue how to do these numbers, a hint would be appreciated
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  2. #2
    Super Member
    Aug 2008
    If the path is given parametrically as $\displaystyle x(t)$ and $\displaystyle y(t)$ then the arc length between $\displaystyle t_1$ and $\displaystyle t_2$ is: $\displaystyle A=\int_{t_1}^{t_2}\sqrt{(x'(t))^2+(y'(t))^2}dt$

    Ok, so you have $\displaystyle \Gamma(t)=e^{-1+2it}$. So that's not too hard to split that up into it's real part (x) and imaginary part (y) right?
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