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
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?