Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 1.7 : Complex Numbers
5. Perform the indicated operation and write your answer in standard form.
\[\left( { - 3 - 9i} \right)\left( {1 + 10i} \right)\]
Hint : You know how to do the operation with polynomials so you can do the operation here! Just recall that you need to be careful to deal with any \(i^{2}\) that might happen to show up in the process.
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.
\[\left( { - 3 - 9i} \right)\left( {1 + 10i} \right) = - 3 - 30i - 9i - 90\left( { - 1} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{87 - 39i}}\]