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Complex Numbers

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Complex number plane: rectangular coordinate plane where the ... similar to multiplying binomials, use FOIL, vertical or horizontal methods, but remember, i*i=1 ... – PowerPoint PPT presentation

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Title: Complex Numbers


1
Complex Numbers
  • Section 5.5
  • Pages 258 - 264

2
Objectives
  • Identify, add, subtract and multiply complex and
    imaginary numbers.

3
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

4
Numbers
5
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

6
Properties of Complex Numbers
  • Associative
  • Commutative
  • Distributive

7
Real World Application
  • Electrical Engineering

8
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)

9
The Load Formula
The load formula uses the real and reactive load
requirements to determine KVA. KVA is the basis
for equipment cost.
10
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.

11
Objectives
  • Identify, add, subtract and multiply complex and
    imaginary numbers.

12
Assignment
  • Pages 262 - 263, problems 3, 6, 9, . . . , 66
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