Chapter 7 - Section 7.7 - Complex Numbers - Exercise Set - Page 463: 67

$17+144i$

Using $i^2=-1$ and $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the expression $ (9+8i)^2 $ is equivalent to \begin{array}{l} (9)^2+2(9)(8i)+(8i)^2 \\= 81+144i+64i^2 \\= 81+144i+64(-1) \\= 17+144i .\end{array}