AN INTRODUCTION TO REAL AND IMAGINARY NUMBERS

A HALF-DAY ON-SITE COURSE

Course Description:

This unique interactive course is designed to provide attendees with a first introduction to real and imaginary numbers.  No prior knowledge of complex numbers is assumed. This course is intended to give participants a working familiarity with the manipulation of simple expressions, and with the confidence to deal with more advanced concepts involving real and imaginary numbers.

The course starts at the very beginning, dealing first with complex numbers, and with their intercombination through addition, subtraction, multiplication, and division.   We then see how to find the real or the imaginary parts of complex numbers, and we manipulate usages of the complex conjugation notation.  Next, we introduce trigonometric functions of complex variables (concentrating on sine and cosine), and the exponential functions of complex arguments. We also learn how to rapidly recall formulas for sines or cosines of sums, differences, or multiples.

During this course, much personal attention will be given to each participant in the class. There will be several short homework sessions during the course, where participants will be able to practice some of the procedures and to review some of the concepts that they had learned. These student activities will be immediately "self-graded" so that each student will be most readily able to assess his/her progress, and further, will be able to identify any special needs. This is intended to be an interactive course, encouraging participation to the fullest extent.

Each idea is explained in clear and simple terms with an emphasis on underlying principles.  Pertinent references and review material are identified. The notes contain copies of each vuegraph used during the course so that participants can spend a maximum amount of time listening and understanding.

Benefits
This course will enable you to:

• Find the real and the imaginary part of a complex number.
• Add, subtract, multiply, and divide complex numbers.
• Factor sums and differences into products of complex numbers.
• Understand exponentiation of a purely imaginary number.
• Appreciate the relationships between circular functions and exponential functions.
Intended Audience
Engineers, technicians, and managers who need a fundamental understanding of real and imaginary numbers, complex numbers, complex functions, etc.

Continuing Education Units (CEU's) available upon request.

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