Suche senden
Hochladen
AA Section 6-8
•
Als ZIP, PDF herunterladen
•
0 gefällt mir
•
405 views
J
Jimbo Lamb
Folgen
Imaginary Numbers
Weniger lesen
Mehr lesen
Bildung
Melden
Teilen
Melden
Teilen
1 von 54
Jetzt herunterladen
Empfohlen
AA Section 6-9
AA Section 6-9
Jimbo Lamb
1.4 complex numbers
1.4 complex numbers
math260
The history of i
The history of i
Kristen Fouss
ComplexNumbers_Part 1
ComplexNumbers_Part 1
Irma Crespo
X2 t01 01 arithmetic of complex numbers (2013)
X2 t01 01 arithmetic of complex numbers (2013)
Nigel Simmons
Pc sinbad cosette
Pc sinbad cosette
Kristen Fouss
X2 T01 01 complex number definitions
X2 T01 01 complex number definitions
Nigel Simmons
5 1 complex numbers-x
5 1 complex numbers-x
math123b
Empfohlen
AA Section 6-9
AA Section 6-9
Jimbo Lamb
1.4 complex numbers
1.4 complex numbers
math260
The history of i
The history of i
Kristen Fouss
ComplexNumbers_Part 1
ComplexNumbers_Part 1
Irma Crespo
X2 t01 01 arithmetic of complex numbers (2013)
X2 t01 01 arithmetic of complex numbers (2013)
Nigel Simmons
Pc sinbad cosette
Pc sinbad cosette
Kristen Fouss
X2 T01 01 complex number definitions
X2 T01 01 complex number definitions
Nigel Simmons
5 1 complex numbers-x
5 1 complex numbers-x
math123b
009 chapter ii
009 chapter ii
aleli ariola
Matlab complex numbers
Matlab complex numbers
Ameen San
An introdcution to complex numbers jcw
An introdcution to complex numbers jcw
jenniech
Complex number
Complex number
Daffodil International University
1.3 Complex Numbers, Quadratic Equations In The Complex Number System
1.3 Complex Numbers, Quadratic Equations In The Complex Number System
guest620260
complex numbers
complex numbers
valour
Complex Numbers
Complex Numbers
swartzje
Maths Project Quadratic Equations
Maths Project Quadratic Equations
Rishabh Dhakarwal
Quadratic equation
Quadratic equation
HOME!
Complex numbers org.ppt
Complex numbers org.ppt
Osama Tahir
Complex Number I - Presentation
Complex Number I - Presentation
yhchung
Complex numbers 2
Complex numbers 2
Dr. Nirav Vyas
Imaginary numbers
Imaginary numbers
SamanthaS13
Geometry Section 1-5
Geometry Section 1-5
Jimbo Lamb
Geometry Section 1-4
Geometry Section 1-4
Jimbo Lamb
Geometry Section 1-3
Geometry Section 1-3
Jimbo Lamb
Geometry Section 1-2
Geometry Section 1-2
Jimbo Lamb
Geometry Section 1-2
Geometry Section 1-2
Jimbo Lamb
Geometry Section 1-1
Geometry Section 1-1
Jimbo Lamb
Algebra 2 Section 5-3
Algebra 2 Section 5-3
Jimbo Lamb
Algebra 2 Section 5-2
Algebra 2 Section 5-2
Jimbo Lamb
Algebra 2 Section 5-1
Algebra 2 Section 5-1
Jimbo Lamb
Weitere ähnliche Inhalte
Andere mochten auch
009 chapter ii
009 chapter ii
aleli ariola
Matlab complex numbers
Matlab complex numbers
Ameen San
An introdcution to complex numbers jcw
An introdcution to complex numbers jcw
jenniech
Complex number
Complex number
Daffodil International University
1.3 Complex Numbers, Quadratic Equations In The Complex Number System
1.3 Complex Numbers, Quadratic Equations In The Complex Number System
guest620260
complex numbers
complex numbers
valour
Complex Numbers
Complex Numbers
swartzje
Maths Project Quadratic Equations
Maths Project Quadratic Equations
Rishabh Dhakarwal
Quadratic equation
Quadratic equation
HOME!
Complex numbers org.ppt
Complex numbers org.ppt
Osama Tahir
Complex Number I - Presentation
Complex Number I - Presentation
yhchung
Complex numbers 2
Complex numbers 2
Dr. Nirav Vyas
Imaginary numbers
Imaginary numbers
SamanthaS13
Andere mochten auch
(13)
009 chapter ii
009 chapter ii
Matlab complex numbers
Matlab complex numbers
An introdcution to complex numbers jcw
An introdcution to complex numbers jcw
Complex number
Complex number
1.3 Complex Numbers, Quadratic Equations In The Complex Number System
1.3 Complex Numbers, Quadratic Equations In The Complex Number System
complex numbers
complex numbers
Complex Numbers
Complex Numbers
Maths Project Quadratic Equations
Maths Project Quadratic Equations
Quadratic equation
Quadratic equation
Complex numbers org.ppt
Complex numbers org.ppt
Complex Number I - Presentation
Complex Number I - Presentation
Complex numbers 2
Complex numbers 2
Imaginary numbers
Imaginary numbers
Mehr von Jimbo Lamb
Geometry Section 1-5
Geometry Section 1-5
Jimbo Lamb
Geometry Section 1-4
Geometry Section 1-4
Jimbo Lamb
Geometry Section 1-3
Geometry Section 1-3
Jimbo Lamb
Geometry Section 1-2
Geometry Section 1-2
Jimbo Lamb
Geometry Section 1-2
Geometry Section 1-2
Jimbo Lamb
Geometry Section 1-1
Geometry Section 1-1
Jimbo Lamb
Algebra 2 Section 5-3
Algebra 2 Section 5-3
Jimbo Lamb
Algebra 2 Section 5-2
Algebra 2 Section 5-2
Jimbo Lamb
Algebra 2 Section 5-1
Algebra 2 Section 5-1
Jimbo Lamb
Algebra 2 Section 4-9
Algebra 2 Section 4-9
Jimbo Lamb
Algebra 2 Section 4-8
Algebra 2 Section 4-8
Jimbo Lamb
Algebra 2 Section 4-6
Algebra 2 Section 4-6
Jimbo Lamb
Geometry Section 6-6
Geometry Section 6-6
Jimbo Lamb
Geometry Section 6-5
Geometry Section 6-5
Jimbo Lamb
Geometry Section 6-4
Geometry Section 6-4
Jimbo Lamb
Geometry Section 6-3
Geometry Section 6-3
Jimbo Lamb
Geometry Section 6-2
Geometry Section 6-2
Jimbo Lamb
Geometry Section 6-1
Geometry Section 6-1
Jimbo Lamb
Algebra 2 Section 4-5
Algebra 2 Section 4-5
Jimbo Lamb
Algebra 2 Section 4-4
Algebra 2 Section 4-4
Jimbo Lamb
Mehr von Jimbo Lamb
(20)
Geometry Section 1-5
Geometry Section 1-5
Geometry Section 1-4
Geometry Section 1-4
Geometry Section 1-3
Geometry Section 1-3
Geometry Section 1-2
Geometry Section 1-2
Geometry Section 1-2
Geometry Section 1-2
Geometry Section 1-1
Geometry Section 1-1
Algebra 2 Section 5-3
Algebra 2 Section 5-3
Algebra 2 Section 5-2
Algebra 2 Section 5-2
Algebra 2 Section 5-1
Algebra 2 Section 5-1
Algebra 2 Section 4-9
Algebra 2 Section 4-9
Algebra 2 Section 4-8
Algebra 2 Section 4-8
Algebra 2 Section 4-6
Algebra 2 Section 4-6
Geometry Section 6-6
Geometry Section 6-6
Geometry Section 6-5
Geometry Section 6-5
Geometry Section 6-4
Geometry Section 6-4
Geometry Section 6-3
Geometry Section 6-3
Geometry Section 6-2
Geometry Section 6-2
Geometry Section 6-1
Geometry Section 6-1
Algebra 2 Section 4-5
Algebra 2 Section 4-5
Algebra 2 Section 4-4
Algebra 2 Section 4-4
Kürzlich hochgeladen
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
Nguyen Thanh Tu Collection
Making and Justifying Mathematical Decisions.pdf
Making and Justifying Mathematical Decisions.pdf
Chris Hunter
Unit-IV- Pharma. Marketing Channels.pptx
Unit-IV- Pharma. Marketing Channels.pptx
VishalSingh1417
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
EduSkills OECD
How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17
Celine George
Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
Celine George
Measures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and Mode
Thiyagu K
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global Impact
PECB
Food Chain and Food Web (Ecosystem) EVS, B. Pharmacy 1st Year, Sem-II
Food Chain and Food Web (Ecosystem) EVS, B. Pharmacy 1st Year, Sem-II
Shubhangi Sonawane
Unit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptx
VishalSingh1417
Key note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdf
Admir Softic
1029 - Danh muc Sach Giao Khoa 10 . pdf
1029 - Danh muc Sach Giao Khoa 10 . pdf
QucHHunhnh
Measures of Dispersion and Variability: Range, QD, AD and SD
Measures of Dispersion and Variability: Range, QD, AD and SD
Thiyagu K
Seal of Good Local Governance (SGLG) 2024Final.pptx
Seal of Good Local Governance (SGLG) 2024Final.pptx
negromaestrong
Holdier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdf
agholdier
Python Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docx
Ramakrishna Reddy Bijjam
ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701
bronxfugly43
PROCESS RECORDING FORMAT.docx
PROCESS RECORDING FORMAT.docx
PoojaSen20
1029-Danh muc Sach Giao Khoa khoi 6.pdf
1029-Danh muc Sach Giao Khoa khoi 6.pdf
QucHHunhnh
On National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan Fellows
Mebane Rash
Kürzlich hochgeladen
(20)
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
Making and Justifying Mathematical Decisions.pdf
Making and Justifying Mathematical Decisions.pdf
Unit-IV- Pharma. Marketing Channels.pptx
Unit-IV- Pharma. Marketing Channels.pptx
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17
Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
Measures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and Mode
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Food Chain and Food Web (Ecosystem) EVS, B. Pharmacy 1st Year, Sem-II
Food Chain and Food Web (Ecosystem) EVS, B. Pharmacy 1st Year, Sem-II
Unit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptx
Key note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdf
1029 - Danh muc Sach Giao Khoa 10 . pdf
1029 - Danh muc Sach Giao Khoa 10 . pdf
Measures of Dispersion and Variability: Range, QD, AD and SD
Measures of Dispersion and Variability: Range, QD, AD and SD
Seal of Good Local Governance (SGLG) 2024Final.pptx
Seal of Good Local Governance (SGLG) 2024Final.pptx
Holdier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdf
Python Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docx
ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701
PROCESS RECORDING FORMAT.docx
PROCESS RECORDING FORMAT.docx
1029-Danh muc Sach Giao Khoa khoi 6.pdf
1029-Danh muc Sach Giao Khoa khoi 6.pdf
On National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan Fellows
AA Section 6-8
1.
Section 6-8
Imaginary Numbers Friday, February 13, 2009
2.
Warmup
Simplify the following: 2 2 () ( ) 1. 2 3 2. −3 2 3. 6 • 15 4. -100 Friday, February 13, 2009
3.
Warmup
Simplify the following: 2 2 () ( ) 1. 2 3 2. −3 2 12 3. 6 • 15 4. -100 Friday, February 13, 2009
4.
Warmup
Simplify the following: 2 2 () ( ) 1. 2 3 2. −3 2 12 18 3. 6 • 15 4. -100 Friday, February 13, 2009
5.
Warmup
Simplify the following: 2 2 () ( ) 1. 2 3 2. −3 2 12 18 3. 6 • 15 4. -100 ≈ 9.49 Friday, February 13, 2009
6.
Warmup
Simplify the following: 2 2 () ( ) 1. 2 3 2. −3 2 12 18 3. 6 • 15 4. -100 ≈ 9.49 ??? Friday, February 13, 2009
7.
Definition Friday, February 13,
2009
8.
Definition
When k > 0, the two solutions to x2 = k are k and − k Friday, February 13, 2009
9.
Big Question Friday, February
13, 2009
10.
What Friday, February 13,
2009
11.
is Friday, February 13,
2009
12.
−k ? Friday, February
13, 2009
13.
Friday, February 13,
2009
14.
What is −k
? Friday, February 13, 2009
15.
Imaginary Number Friday, February
13, 2009
16.
Imaginary Number
i = −1 Friday, February 13, 2009
17.
Theorem Friday, February 13,
2009
18.
Theorem
If k > 0, −k = −1 k = i k Friday, February 13, 2009
19.
Example 1
Solve. x2 = -100 Friday, February 13, 2009
20.
Example 1
Solve. x2 = -100 2 x = ± −100 Friday, February 13, 2009
21.
Example 1
Solve. x2 = -100 2 x = ± −100 x = ± −1 100 Friday, February 13, 2009
22.
Example 1
Solve. x2 = -100 2 x = ± −100 x = ± −1 100 x=± Friday, February 13, 2009
23.
Example 1
Solve. x2 = -100 2 x = ± −100 x = ± −1 100 x = ±i Friday, February 13, 2009
24.
Example 1
Solve. x2 = -100 2 x = ± −100 x = ± −1 100 x = ± i 10 Friday, February 13, 2009
25.
Example 1
Solve. x2 = -100 2 x = ± −100 x = ± −1 100 x = ± i 10 x = ±10i Friday, February 13, 2009
26.
Example 2
Show that i 7 is a square root of -7. Friday, February 13, 2009
27.
Example 2
Show that i 7 is a square root of -7. 2 (i 7 ) Friday, February 13, 2009
28.
Example 2
Show that i 7 is a square root of -7. 2 (i 7 ) 2 ( )( ) 2 7 =i Friday, February 13, 2009
29.
Example 2
Show that i 7 is a square root of -7. 2 (i 7 ) 2 ( )( 7 ) 2 =i = ( −1) ( 7 ) Friday, February 13, 2009
30.
Example 2
Show that i 7 is a square root of -7. 2 (i 7 ) 2 ( )( 7 ) 2 =i = ( −1) ( 7 ) = −7 Friday, February 13, 2009
31.
Example 3
Simplify. b. (6i)(4i) a. −4 − −49 Friday, February 13, 2009
32.
Example 3
Simplify. b. (6i)(4i) a. −4 − −49 = 2i Friday, February 13, 2009
33.
Example 3
Simplify. b. (6i)(4i) a. −4 − −49 = 2i - Friday, February 13, 2009
34.
Example 3
Simplify. b. (6i)(4i) a. −4 − −49 = 2i - 7i Friday, February 13, 2009
35.
Example 3
Simplify. b. (6i)(4i) a. −4 − −49 = 2i - 7i = -5i Friday, February 13, 2009
36.
Example 3
Simplify. b. (6i)(4i) a. −4 − −49 = 2i - 7i = 24i2 = -5i Friday, February 13, 2009
37.
Example 3
Simplify. b. (6i)(4i) a. −4 − −49 = 2i - 7i = 24i2 = -5i = 24(-1) Friday, February 13, 2009
38.
Example 3
Simplify. b. (6i)(4i) a. −4 − −49 = 2i - 7i = 24i2 = -5i = 24(-1) = -24 Friday, February 13, 2009
39.
Example 3
Simplify. −25 d. c. −32 + −2 −81 Friday, February 13, 2009
40.
Example 3
Simplify. −25 d. c. −32 + −2 −81 2 = −16g + −2 Friday, February 13, 2009
41.
Example 3
Simplify. −25 d. c. −32 + −2 −81 2 = −16g + −2 = −16 2 + −2 Friday, February 13, 2009
42.
Example 3
Simplify. −25 d. c. −32 + −2 −81 2 = −16g + −2 = −16 2 + −2 = 4i 2 + i 2 Friday, February 13, 2009
43.
Example 3
Simplify. −25 d. c. −32 + −2 −81 2 = −16g + −2 = −16 2 + −2 = 4i 2 + i 2 = 5i 2 Friday, February 13, 2009
44.
Example 3
Simplify. −25 d. c. −32 + −2 −81 2 = −16g + −2 5i = −16 2 + −2 = 9i = 4i 2 + i 2 = 5i 2 Friday, February 13, 2009
45.
Example 3
Simplify. −25 d. c. −32 + −2 −81 2 = −16g + −2 5i = −16 2 + −2 = 9i = 4i 2 + i 2 5 = 5i 2 = 9 Friday, February 13, 2009
46.
Example 4
Simplify. −36 −64 Friday, February 13, 2009
47.
Example 4
Simplify. −36 −64 = 6ig8i Friday, February 13, 2009
48.
Example 4
Simplify. −36 −64 = 6ig8i 2 = 48i Friday, February 13, 2009
49.
Example 4
Simplify. −36 −64 = 6ig8i 2 = 48i = −48 Friday, February 13, 2009
50.
Example 4
Simplify. −36 −64 = 6ig8i 2 = 48i = −48 **NOTE** Friday, February 13, 2009
51.
Example 4
Simplify. −36 −64 = 6ig8i 2 = 48i = −48 **NOTE** Do NOT combine radicals that have negatives inside! Friday, February 13, 2009
52.
Example 4
Simplify. −36 −64 = 6ig8i 2 = 48i = −48 **NOTE** Do NOT combine radicals that have negatives inside! −36 −64 ≠ 2304 = 48 Friday, February 13, 2009
53.
Homework Friday, February 13,
2009
54.
Homework
p. 391 #1 - 29 “They can because they think they can.” - Virgil Friday, February 13, 2009
Hinweis der Redaktion
Jetzt herunterladen