Determine whether the following pairs of paths are rectifiable and equivalent: $\gamma_1:[0,2\pi]\to\Bbb C$, given by $\gamma_1(t)=e^{it}$ for each $t\in[0,2\pi]$, and $\gamma_2:[0,4\pi]\to\Bbb C$, given by $\gamma_2(t)=e^{it}$ for each $t\in[0,4\pi]$.
I managed to show that these two paths are rectifiable. I am having difficulty in showing the equivalence part.
I tried to find a change of parameter $\phi$, but I cannot find one. I tried the $\phi(t)=t/2$, but this doesn't work since it doesn't satisfy $\gamma_2=\gamma_1\circ\phi$.
Could someone kindly help? Thanks so much!