5. Perform the indicated operation and write your answer in standard form.
\[\left( { - 3 - 9i} \right)\left( {1 + 10i} \right)\]We know how to multiply two polynomials and so we also know how to multiply two complex numbers. All we need to do is "foil" the two complex numbers to get,
\[\left( { - 3 - 9i} \right)\left( {1 + 10i} \right) = - 3 - 30i - 9i - 90{i^2}\]All we need to do to finish the problem is to recall that \({i^2} = - 1\). Upon using this fact we can finish the problem.
\[\left( { - 3 - 9i} \right)\left( {1 + 10i} \right) = - 3 - 30i - 9i - 90\left( { - 1} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{87 - 39i}}\]