Your answer is correct... [tex]i^2=-1[/tex], so
[tex](3+i)(i^2+8i-2)=(3+i)(-3+8i)[/tex]
Then distributing [tex]3+i[/tex] to both terms on the right gives
[tex](3+i)(-3)+(3+i)(8i)=(-9-3i)+(24i+8i^2)=-9-3i+24i-8=-17+21i[/tex]
