The expression is given to be:
[tex]\left(8+5i\right)\left(6+3i\right)[/tex]
To expand the expression, we can apply the complex arithmetic rule given to be:
[tex]\left(a+bi\right)\left(c+di\right)=\left(ac-bd\right)+\left(ab+bc\right)i[/tex]
Taking values of a, b, c, and d to be:
[tex]\begin{gathered} a=8 \\ b=5 \\ c=6 \\ d=3 \end{gathered}[/tex]
We can solve it to give:
[tex]\begin{gathered} \left(8+5i\right)\left(6+3i\right)=\left(8\cdot\:6-5\cdot\:3\right)+\left(8\cdot\:3+5\cdot\:6\right)i \\ \left(8+5i\right)\left(6+3i\right)=33+54i \end{gathered}[/tex]
ANSWER
[tex](8+5\imaginaryI)(6+3\imaginaryI)=33+54\imaginaryI[/tex]
OPTION A is the correct option.
