Properties of the Complex Set

The set of complex numbers is denoted . Just like any other number set there are rules of operation.

The sum and difference of complex numbers is defined by adding or subtracting their real components ie:

The communitive and distributive properties hold for the product of complex numbers ie:

When dividing two complex numbers you are basically rationalizing the denominator of a rational expression. If we have a complex number defined as z =a+bi then the conjuate would be . See the following example:

Example:

Conjugates

The geometric inperpretation of a complex conjugate is the reflection along the real axis. This can be seen in the figure below where z = a+bi is a complex number. Listed below are also several properties of conjugates.

Properties:
                          



credit to :
http://algebra.nipissingu.ca/tutorials/complex_numbers.html

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