
To add two complex numbers just combine like terms.


To subtract two complex numbers just combine like terms.


To multiply a real times a complex just distribute.


To multiply an imaginary times a complex just distribute and then
use i^{ 2} = − 1.


To multiply two complex numbers just distribute and then
use i^{ 2} = − 1.


Multiplying a complex number by its complex conjugate
(defined above) always results in a positive real number
because the crossterms cancel.


To divide a complex number by a real just break the fraction
into two parts.


The reciprocal of i is − i.
You can verify this by crossmultiplying.


To divide a complex number by an imaginary number just break
the fraction into two parts and then use the fact that the
reciprocal of i is − i.


To simplify the reciprocal of a complex number multiply
numerator and denominator by the complex conjugate of the denominator.
This is designed to produce a positive real number in the denominator
which can then be divided into each term of the numerator.


A shortcut for the previous example is to replace a reciprocal by the
complex conjugate in the numerator over a Pythagoras type sum of squares
in the denominator.


To divide two complex numbers, multiply the numerator and denominator
by the complex conjugate of the denominator. This produces a Pythagoras
type sum of squares in the denominator and two complex numbers in
the numerator that can be multiplied as described previously.
