5-4 Complex Numbers (Day 1) - PowerPoint PPT Presentation

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5-4 Complex Numbers (Day 1)

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5-4 Complex Numbers (Day 1) Objective: CA 5.0 Students demonstrate knowledge of how real number and complex numbers are related both arithmetically and graphically. – PowerPoint PPT presentation

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Title: 5-4 Complex Numbers (Day 1)


1
5-4Complex Numbers(Day 1)
Objective CA 5.0 Students demonstrate knowledge
of how real number and complex numbers are
related both arithmetically and graphically.
2
Not all quadratic equations have real number
solutions.
has no real number solutions because the square
of any real number x is never negative.
3
To overcome this problem, mathematicians created
an expanded system of numbers using the imaginary
unit.
The imaginary unit i can be used to write the
square root of any negative number.
4
The square root property of a negative number
property
1. If r is a positive real number then
5
2. By property (1) it follows that
6
Example 1 Solve
7
A complex number written in standard form is a
number a bi where a and b are real numbers.
The number a is the real part of the complex
number, the number bi is the imaginary part.
If b ? 0 then a bi is an imaginary number
If a 0 and b ? 0 then a bi is a pure imaginary
number.
8
Every complex number corresponds to a point in
the complex plane.
Keep in mind
  • a is the real part (x coordinate)
  • bi is the imag. part (y-coordinate)

9
Example 2 
2-3i (2, -3)
-32i (-3, 2)
4i (0, 4)
10
Two complex numbers a bi and c di are equal
if and only if ac and bd
Sum of complex numbers
Difference of complex numbers
11
Simplify
v-18 v-32
iv18 iv32
3iv2 4iv2
7iv2
12
Example 3 Write the expression as a complex
number in standard form.
4 i 3 2i
7 i
13
Example 4
7 5i - 1 5i
6 0i
6
14
Example 5
6 2 - 9i - 8 4i
-9i 4i
-5i
15
Multiplying Complex Numbers
To multiply complex numbers use the distributive
property or the FOIL method.
16
Example 5 Write each expression as a complex
number in standard form.
1.
17
Example 6
18
Example 7
19
Homework Accelerated Math Objective Add
Subtract/Multiply Complex Numbers
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