Page

**1**

Slide 1

Complex Numbers

Lesson 3.3

Slide 2

By definition

Consider powers if i

Slide 3

Now we can handle quantities that occasionally show up in mathematical solutions

What about

Slide 4

Combine real numbers with imaginary numbers

a + bi

Examples

Slide 5

Write these complex numbers in standard form a + bi

Slide 6

Complex numbers can be combined with

addition

subtraction

multiplication

division

Consider

Slide 7

Operations on Complex Numbers

Division technique

Multiply numerator and denominator by the conjugate of the denominator

Slide 8

Possible result

Reset mode Complex format to Rectangular

Now calculator does desired result

Slide 9

Complex Numbers on the Calculator

Operations with complex on calculator

Make sure to use the correct character for i. Use 2nd-i

Slide 10

Consider

It is tempting to combine them

The multiplicative property of radicals only works for positive values under the radical sign

Instead use imaginary numbers

Slide 11

Try It Out

Use the correct principles to simplify the following:

Slide 12

Consider the expression under the radical in the quadratic formula

This is known as the discriminant

What happens when it is

Positive and a perfect square?

Positive and not a perfect square?

Zero

Negative ?

Return of the

Slide 13

Consider the solution to

Note the graph

No intersections with x-axis

Using the solve and csolve functions

Slide 14

Go to page:

1 2

1 2

- The Imaginary Number
- Using
- Complex Numbers
- Try It Out
- Operations on Complex Numbers
- Complex Numbers on the Calculator
- Warning
- The Discriminant
- Example
- Fundamental Theorem of Algebra
- Conjugate Zeroes Theorem
- Assignment

- Friction
- Ch 9 Nuclear Radiation
- Magnetic field uses sound waves to ignite sun's ring of fire
- Sound
- Radiation
- Newton’s third law of motion
- Newton’s Law of Gravity

© 2010-2023 powerpoint presentations