Question

Find the product of these complex numbers.(8 + 5i)(6 + 3i) =A.33 + 54iB.63 + 54iC.48 + 15iD.48 - 15i

Answer 1

The expression is given to be:

`\left(8+5i\right)\left(6+3i\right)`

To expand the expression, we can apply the complex arithmetic rule given to be:

`\left(a+bi\right)\left(c+di\right)=\left(ac-bd\right)+\left(ab+bc\right)i`

Taking values of a, b, c, and d to be:

`\begin{gathered} a=8 \\ b=5 \\ c=6 \\ d=3 \end{gathered}`

We can solve it to give:

`\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}`

ANSWER

`(8+5\imaginaryI)(6+3\imaginaryI)=33+54\imaginaryI`

OPTION A is the correct option.