Solution:
To find the product of the complex numbers given:
[tex](5+6i)(3-3i)[/tex]
we multiply the terms in the second parentheses by each term in the first parentheses.
Thus, we have
[tex]\begin{gathered} 5(3-3i)+6i(3-3i) \\ open\text{ parentheses,} \\ 15-15i+18i-18i^2 \\ but \\ i^2=-1 \\ thus, \\ 15-15i+18i-18(-1) \\ =15-15i+18i+18 \\ collect\text{ like terms,} \\ (15+18)+i(18-15) \\ =33+3i \end{gathered}[/tex]
Hence, the product is
[tex]33+3i[/tex]
The correct option is D
