A complex number is any number that can be written as <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle mathcolor="#1fab54"><mi>a</mi></mstyle><mo>+</mo><mstyle mathcolor="#11accd"><mi>b</mi></mstyle><mi>i</mi></mrow><annotation encoding="application/x-tex">\greenD{a}+\blueD{b}i</annotation></semantics></math>a+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i, where <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math>ii is the imaginary unit and <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle mathcolor="#1fab54"><mi>a</mi></mstyle></mrow><annotation encoding="application/x-tex">\greenD{a}</annotation></semantics></math>astart color #1fab54, a, end color #1fab54 and <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle mathcolor="#11accd"><mi>b</mi></mstyle></mrow><annotation encoding="application/x-tex">\blueD{b}</annotation></semantics></math>bstart color #11accd, b, end color #11accd are real numbers.
When
multiplying complex numbers, it's useful to remember that the
properties we use when performing arithmetic with real numbers <style type="text/css">
re(3): Nothing - or 1.... or -1?
