# Why are these loops homotopics?

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 $$a,b in mathbb{Z}$$?