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Complex Numbers

- Section 5.5
- Pages 258 - 264

Objectives

- Identify, add, subtract and multiply complex and

imaginary numbers.

Definitions

- Imaginary numbers numbers with v-1 (i) as a

factor v-25 5i - Complex numbers numbers that are the sum of a

real number and an imaginary number 73i - Complex number plane rectangular coordinate

plane where the real part of a complex number is

graphed on the horizontal axis and the imaginary

part is graphed on the vertical axis - Standard form a bi

Numbers

Operations With Complex Numbers

- Addition and subtraction add/subtract real

parts, then add/subtract imaginary parts - Multiplication similar to multiplying binomials,

use FOIL, vertical or horizontal methods, but

remember, ii1

Properties of Complex Numbers

- Associative
- Commutative
- Distributive

Real World Application

- Electrical Engineering

Imaginary Reactive

- Electrical engineers often use complex numbers to

represent electrical load on AC circuits. - The real part of the complex number represents

real load (KW) which corresponds to fuel costs - The imaginary part of the complex number

represents reactive load (KVAR)

The Load Formula

The load formula uses the real and reactive load

requirements to determine KVA. KVA is the basis

for equipment cost.

Power Factor

- The ratio of KW/KVA is called the power factor

and is often used to describe the load

requirements of a system. - When the reactive load is zero, KWKVA, the power

factor is one and the system is operating

efficiently. - Capacitors have no real load and a negative

reactive load. They are added to the system to

achieve a power factor of one.

Objectives

- Identify, add, subtract and multiply complex and

imaginary numbers.

Assignment

- Pages 262 - 263, problems 3, 6, 9, . . . , 66

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presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

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