Trigonometry - Complex Numbers and De Moivre’s Theorem

Complex Numbers and De Moivre’s Theorem

Topic Review on "Title":

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.

De Moivre’s Formula:

where n is an integer.

Exponential form of complex number:
where is the modulus of and is its argument.

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"Title" Tutorial Summary :

This tutorial is all about complex numbers, their operations and their properties. Complex numbers are visually introduced with the use of examples and relations to rectangular coordinates. The simplification of roots of negative numbers is shown with the use of theorems such as De Moivre’s Theorem.

The trigonometric and exponential formulation is made possible with an introduction of the complex number definition in standard form. The simplification division of complex numbers is performed with the use of exponential forms.

Tutorial Features:

Specific Tutorial Features:
• Step by step examples of the different aspects of complex numbers and examples of them.
• Concept based questions are given to ensure that the most important ideals have been learned.

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.

"Title" Topic List:

Complex Numbers
          Definition of complex numbers
          The imaginary part of a complex number
          The complex conjugate and its definition
          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
          De Moivre’s Formula
          Exponential form of a complex number

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