The given expression is:
[tex](7+9i)(8-10i)[/tex]Expand the binomial, noting that for a complex number, i²=-1:
[tex]\begin{gathered} (7+9i)(8-10i)=7(8-10i)+9i(8-10i) \\ \Rightarrow(7+9i)(8-10i)=56-70i+72i-90i^2 \end{gathered}[/tex]Substitute i²=-1 into the expression:
[tex]\begin{gathered} (7+9i)(8-10i)=56-70i+72i-90i^2 \\ \Rightarrow(7+9i)(8-10i)=56-70i+72i-90(-1)=56-70i+72i+90 \\ \text{Collect like terms and simplify:} \\ \Rightarrow(7+9i)(8-10i)=56+90-70i+72i=146+2i \end{gathered}[/tex]The correct answer is option 4.
