Page 300
Download
1 / 24

Page 300 - PowerPoint PPT Presentation


  • 135 Views
  • Uploaded on

Page 300. Complex Solutions. Complex Numbers. Complex Numbers are numbers that are associated with a second real number with an ordered pair a + b i Conjugate is the complex number’s opposite sign Example: 2 + 3 i ‘s conjugate is 2 – 3 i

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Page 300' - nhi


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Page 300
Page 300

4.5 - Complex Numbers



Complex solutions

Complex Solutions

4.5 - Complex Numbers


Complex numbers
Complex Numbers

Complex Numbersare numbers that are associated with a second real number with an ordered pair

a + b i

Conjugate is the complex number’s opposite sign

Example: 2 + 3i ‘s conjugate is 2 – 3i

Remember: NO IMAGINARY NUMBERSin the denominator

SIMPLIFY RADICALS FIRST then OPERATE

Imaginary Number

Real Number

4.5 - Complex Numbers


Example 1
Example 1

Find the values of x and y that make the equation 4x + 10i= 2 – (4y)itrue.

Real parts

4x + 10i = 2 – (4y)i

Imaginary parts

4.5 - Complex Numbers


Example 2
Example 2

Find the values of x and y that make the equation 2x – 6i= –8 + (20y)itrue.

4.5 - Complex Numbers


Your turn
Your Turn

Find the values of x and y that make the equation

true.

4.5 - Complex Numbers


Imaginary numbers
Imaginary Numbers

Rules with Imaginaries:

i1 = i

i2 = –1

Answers CAN have an i but CAN NOT have two i’s

Two i’s make –1

4.5 - Complex Numbers


Example 3
Example 3

Solve the equation, 5x2 + 90 = 0

4.5 - Complex Numbers


Your turn1
Your Turn

Solve the equation, 9x2 + 25 = 0

4.5 - Complex Numbers


Example 4
Example 4

Solve the equation, 3x2 – 2x + 5 = 0

4.5 - Complex Numbers


Your turn2
Your Turn

Solve the equation, 2x2 + x + 3 = 0

4.5 - Complex Numbers


Cube roots
Cube Roots

4.5 - Complex Numbers


Sum and difference of cube roots
Sum and Difference of Cube Roots

  • Take the GCF Out

  • Put the equation into perfect cubes

  • Put the bases of the cubes into parentheses

  • Refer to the bases in the parentheses and follow the format of S1OMAS2

S1 – Square the first base

O – Take Opposite of the original problem’s sign

M – Multiply the first and second base (leave the signs alone)

A – Put addition sign

S2 – Square the second base

4.5 - Complex Numbers


Example 5
Example 5

Solve the equation, x3 + 27 = 0

4.5 - Complex Numbers


Example 6
Example 6

Solve the equation, x3 – 27 = 0

4.5 - Complex Numbers


Example 7
Example 7

Solve the equation, x3 – 1 = 0

4.5 - Complex Numbers


Your turn3
Your Turn

Solve the equation, x3 + 64 = 0

4.5 - Complex Numbers


Review
Review

Rationalize

What is the problem with the bottom?

We try to get rid of the radicals on the bottom so the bottom will be even

With the CONJUGATE

4.5 - Complex Numbers


Example 71
Example 7

Rationalize

What is the problem with the bottom?

We try to get rid of the radicals on the bottom so the bottom will be even

With the CONJUGATE

4.5 - Complex Numbers


Example 8
Example 8

Rationalize

4.5 - Complex Numbers


Example 9
Example 9

Rationalize

4.5 - Complex Numbers


Your tur n
Your Turn

Rationalize

4.5 - Complex Numbers


Assignment
Assignment

Page 300

23-31 odd, 55-67 odd

4.5 - Complex Numbers


ad