What it means for a complex number to have absolute value 1, is: given $a+bi \in \C$, we say that $a+bi$ has absolute value $1$ if $a^2+b^2 =1$.
We can see that the function in your hint, $e^{2\pi (ix)} = \cos{2 \pi x} + i\sin{2 \pi x}$. This function is well-defined, as it maps elements of...