The Complex Number System
BASIC SET THEORY
Set – A set is a group of items or collection of objects.
Element (member) – The objects or items that make up a set are called elements.
means “is an element of”
means “is not an element of”
Example: Given: Set A = {8, 6, 4}
4A
7A
Subset – A subset is a part of a set.
 means “is a subset of”
 means “is not a subset of”
Example: Given: Set A = {2, 4, 6, 8, 10, …} Set B = {6, 12, 30} Set C = {1, 3, 5}
BA
CA
Venn diagram – A Venn diagram is an illustration that is used to show relationships between sets.
SUBSETS OF THE COMPLEX NUMBER SYSTEM
The Complex Number System

Imaginary
Numbers
Q
J
W
N
Irrational
Numbers
Natural Numbers – The set of numbers that is used in counting, sometimes referred to as N.
N = {1, 2, 3, 4 ,…}
Whole Numbers – The set of natural numbers and zero, sometimes referred to as W.
W = {0, 1, 2, 3, 4 ,…}
Integers – The set of whole numbers and their opposites, sometimes referred to as J or Z.
J = {…, – 3, – 2, – 1, 0, 1, 2, 3, 4 ,…}
Rational Numbers – A rational number is any number that can be expressed in the form of a , where a
b
and b are integers and b ≠ 0. This set is sometimes referred to as Q. Any rational number can be written
as either a terminating decimal or a repeating decimal.
Terminating Decimal –A decimal number with only a finite number of nonzero digits after the
decimal point.
Repeating Decimal –A decimal number with digit or group of digits after the decimal point that
repeats indefinitely. A bar is placed over the repeating pattern to identify a repeating decimal.
Irrational Numbers – Numbers whose decimal part never terminates or repeats. Irrational numbers
cannot be expressed in the form of a , where a and b are integers and b ≠ 0.
b
Real Numbers – The set of rational numbers together with the set of irrational numbers; numbers that
have a place on the number line. This set is sometimes referred to as .
Imaginary Numbers – Numbers that do not have a place on the number line. These numbers are also
called complex numbers.