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