Chapter 6.4, Problem 13E

Let $\left\{u_1,...,u_n\right\}$ be an orthonormal basis for a complex inner product space V, and let
$\begin{array}{l}z=a_1{u}_1+a_2{u}_2+\cdots +a_n{u}_n\\ w=b_1{u}_1+b_2{u}_2+\cdots +b_n{u}_n\end{array}$
Show that
$\langle z,w\rangle ={\displaystyle \underset{i=1}{\overset{n}{\sum }}\overline{b_i}{a}_i}$