Solution
= Solution
The nonzero coefficients and part a(ii) give unique elements $h\in C(t)$ and $h^*\in C(t^*)$ such that
$$
\{u\}=h\{t\}=h^*\{t^*\}.
$$
Part i gives $h=h^*=:k$, so $k\in C(t)\cap C(t^*)$. Both coefficients are then $\operatorname{sgn}(k)$ and hence are equal.