For each $z in mathbb{Z}$, let $omega_z:(0,1) to S^1$ given by $omega_{z}(t)=(cos(2pi z t), sin(2 pi z t))$. How I can prove that $omega_{a+b}$ and $omega_a * omega_b$ are homotopics, for each $a,b in mathbb{Z}$?

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# Why are these loops homotopics?

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For each $z in mathbb{Z}$, let $omega_z:(0,1) to S^1$ given by $omega_{z}(t)=(cos(2pi z t), sin(2 pi z t))$. How I can prove that $omega_{a+b}$ and $omega_a * omega_b$ are homotopics, for each $a,b in mathbb{Z}$?

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