How to show that two functions are fixed homotopic

Question

I have two functions $\gamma_1=exp(i*t) $and $\gamma_2=exp(-i*t) $ for all t in [$0;\pi].$

How do I show that they are fixed homotopic?

Kind regards

Answer 1

Define $\gamma_a(t):=e^{(3-2a)it}$.

In this way $\gamma_1= "your" \gamma_1$ and $\gamma_2= "your" \gamma_2$ !