Basic Algebraic Properties of Complex Numbers

The properties of addition and multiplication of complex numbers turn out to be exactly the same in kind as the familiar properties of addition and multiplication of real numbers — complex numbers form what is called a field, just as the reals do. This section lists the basic algebraic properties side by side (addition on the left, multiplication on the right) and verifies two of the less obvious ones directly from the definitions: the commutative law for addit …