Complex analysis

**Kai** · October 5th 2008, 09:58 AM

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

**shawsend** · October 5th 2008, 01:29 PM

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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