Complex NUMBERS
Polar Form of Complex Numbers
Rev.S08
Learning Objectives
Upon completing this module, you should be able to:
1.
Identify and simplify imaginary and complex
numbers.
Add and subtract complex numbers.
Simplify powers of i.
Multiply complex
Complex NUMBERS
Polar Form of Complex Numbers
Rev.S08
Learning Objectives
Upon completing this module, you should be
able to:
1. Identify and simplify imaginary and complex
numbers.
2. Add and subtract complex numbers.
3. Simplify powers of i.
4. Multiply
The Complex
Plane;
DeMoivre's
Theorem
Remember a complex number has a real part and an
imaginary part. These are used to plot complex
numbers on a complex plane.
z x yi
z x y
2
Imaginary
Axis
2
z x yi
z
x
y
Real
Axis
The magnitude or modulus
of z denoted
The Complex
Plane;
DeMoivre's
Theorem
Remember a complex number has a real part and an
imaginary part. These are used to plot complex
numbers on a complex plane.
z x yi
2
z x y
Imaginary
Axis
z
x
2
z x yi
y
Real
Axis
The magnitude or modulus
of z denoted
Adding, Subtracting, Multiplying
And Dividing Complex Numbers
Describe any number in the complex number system.
Complex Numbers (a + bi)
Natural (Counting) Numbers
Imaginary #s(-1)
Was an Italian mathematician
(hydraulic engineer) who wrote
an influential
Introduction to Complex Numbers
(-1)
Adding, Subtracting, Multiplying
And Dividing Complex Numbers
Describe any number in the complex number system.
Complex Numbers (a + bi)
Natural (Counting) Numbers
Whole Num
s
Integer
bers
bers
m
u
N
l
Rationa
ers
b
m
Section 3
1
Definition of a function
A function is a rule which takes an element from a set
and maps it to a UNIQUE element in another set.
2
Function terminology
f maps R to Z
Domain
R
f
Z
Co-domain
f(4.3)
4
4.3
Pre-image of 4
Image of 4.3
3
More functi
Section 2
1
Introduction
Certain combinations of relation properties are very useful
We wont have a chance to see many applications in this course
In this set we will study equivalence relations
A relation that is reflexive, symmetric and transitive
Functions
Section 3
1
Definition of a function
A function is a rule which takes an element
from a set and maps it to a UNIQUE element
in another set.
2
Function terminology
f maps R to Z
Domain
R
f
Z
Co-domain
f(4.3)
4
4.3
Pre-image of 4
Image of 4.3
3
Mo
Set Theory
Section 1
1
Set Theory - Definitions and notation
A set is an unordered collection of objects referred to as
elements.
A set is said to contain its elements.
Different ways of describing a set.
1 Explicitly: listing the elements of a set
c
Equivalence Relations
Section 2
1
Introduction
Certain combinations of relation properties are
very useful
We wont have a chance to see many applications in this
course
In this set we will study equivalence relations
A relation that is reflexive, symmet
Section 1
1
Set Theory - Definitions and notation
A set is an unordered collection of objects referred to as elements.
A set is said to contain its elements.
Different ways of describing a set.
1 Explicitly: listing the elements of a set
cfw_1, 2, 3