Question

What is the value of (7 + 2i)(3 - i)?

Answer 1

There are two ways to work this out: normal variables or using "imaginary" numbers.

Normal variables:
$(7+2i)(3-i)\\(7*3)+[7*(-i)]+(3*2i)+[2i*(-i)]\\21-7i+6i-2i^{2}\\\\21-i-2i^{2}$

Imaginary numbers:
Using the result from earlier:
$21-i-2i^{2}$
Now since $i = \sqrt{-1}$, then the expression becomes:
$21-i-2i^{2}\\21-i-2(\sqrt{-1})^{2}\\21-i+(-2)(-1)\\21-i+2\\\\23-i$