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Math Help - Complex analysis

  1. #1
    Kai
    Kai is offline
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    Apr 2008
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    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
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    If the path is given parametrically as x(t) and y(t) then the arc length between t_1 and t_2 is: A=\int_{t_1}^{t_2}\sqrt{(x'(t))^2+(y'(t))^2}dt

    Ok, so you have \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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