Let X be a topological space, and let $x_0$ be a point of X. Show that if $\lambda_1$ and $\lambda_2$ in $\pi(X; x_0)$ have the same image under $\pi(X; x_0) \rightarrow [S^1;X]$, then $\lambda_1$ and $\lambda_2$ are conjugate. (Conjugate in the group sense).
I'm confused as to what the images look like in $[S^1; X]$