Title: 5-4 Complex Numbers (Day 1)
15-4Complex Numbers(Day 1)
Objective CA 5.0 Students demonstrate knowledge
of how real number and complex numbers are
related both arithmetically and graphically.
2Not all quadratic equations have real number
solutions.
has no real number solutions because the square
of any real number x is never negative.
3To 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.
4The square root property of a negative number
property
1. If r is a positive real number then
52. By property (1) it follows that
6Example 1 Solve
7A 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.
8Every 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)
9Example 2
2-3i (2, -3)
-32i (-3, 2)
4i (0, 4)
10Two complex numbers a bi and c di are equal
if and only if ac and bd
Sum of complex numbers
Difference of complex numbers
11Simplify
v-18 v-32
iv18 iv32
3iv2 4iv2
7iv2
12Example 3 Write the expression as a complex
number in standard form.
4 i 3 2i
7 i
13Example 4
7 5i - 1 5i
6 0i
6
14Example 5
6 2 - 9i - 8 4i
-9i 4i
-5i
15Multiplying Complex Numbers
To multiply complex numbers use the distributive
property or the FOIL method.
16Example 5 Write each expression as a complex
number in standard form.
1.
17Example 6
18Example 7
19Homework Accelerated Math Objective Add
Subtract/Multiply Complex Numbers