The Magnitude of a vector:
Let be a vector then .

The dot product of vectors:

• Let and be two vectors then the dot product of V and U is equal to:
• .

Definition of a complex number:

• A complex number is a number of the standard form where a and b are real numbers and .

The complex conjugate:

• The conjugate of a complex number is a complex number equal to .

The complex plane:
The two-dimensional Cartesian coordinate system where a complex number is viewed as a point.

DeMoivre’s Formula:

• where n is an integer.

Exponential form of complex number:

• where is the modulus of and  is its argument.

Flash Movie	Flash Game	Flash Card
Core Concept Tutorial	Problem Solving Drill	Review Cheat Sheet

Vectors are common quantities that are used in mathematics and in other field of studies. The properties of vectors are discussed in the examples and their use in application problems. The graphical representation of vectors allows for the introduction of the magnitude of a vector.

Complex numbers are introduced in this part of tutorial along with their properties such as the addition, subtraction, multiplication and division of complex numbers. Other representations of complex numbers are presented such as the trigonometric and the exponential ones. Famous formulas such as De Moivre’s Formulas are used in examples to calculate complex numbers.

Specific Tutorial Features:

• Graphical illustration of the operations of vectors and the formulation of complex numbers.
• Diagrams showing the features of vectors.
• Graphical representation of complex numbers.
• The use of true or false questions to verify understanding of the complex number properties.

Series Features:

• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
• Definition slides introduce terms as they are needed.
• Visual representation of concepts
• Animated examples—worked out step by step
• A concise summary is given at the conclusion of the tutorial.

Definition of a vector
Magnitude of a vector
Addition of vectors
Opposite vectors
Vector dot product
Complex Numbers
Definition of complex numbers
The imaginary unit
The complex conjugate
Addition of complex numbers
Subtraction of complex numbers
Multiplying complex numbers
Multiplying a complex number and its conjugate
Dividing complex numbers
Trigonometric formulation of complex numbers
DeMoivre’s Formula
Exponential form of a complex number