Download presentation

Presentation is loading. Please wait.

Published byJoslyn Turnage Modified over 3 years ago

2
p. 99 only (for now)

3
(3i)(4i) i(2i)(-4i) √-10 ∙ √-15 YOU MUST TAKE OUT THE i FIRST!!!

4
(4i)(-5i)(3i)(i)

5
x 2 – 16 = 0 3x 2 + 48 = 0 2x 2 + 12 = 0 6x 2 + 72

6
5x 2 = -125

7
a + bi a is the real part b is the imaginary part

8
2i + 3i (3 + 5i) + (6 – 10i) (5 – 2i) – (-4 – i)

9
(3 – 2i) – (6 + 3i)

10
(2 – i)(3 + 4i) (5 – 2i)(7 – i) (2 – i)(2 + i)

11
(5 + i)(5 – i)

12
What are imaginary numbers? What are complex numbers? How are they similar and different? THINK silently for 30 seconds. PAIR discuss with your partner for 30 seconds. SHARE with the class

13
Finish the problems that were assigned on p. 113. We will go over the answers in a few minutes.

14
Honors Algebra II

15
Arab Empire (632-end of 13 th century) Main source of knowledge between Greeks and European Renaissance Baghdad established as center of wisdom and learning (9 th century) Many contributions to the study of algebra (800-1450 )

16
“In the foremost rank of mathematicians of all time stands Al-Khwarizmi. He composed the oldest works on arithmetic and algebra. They were the principal source of mathematical knowledge for centuries to come in the East and the West. The work on arithmetic first introduced the Hindu numbers to Europe, as the very name algorism signifies; and the work on algebra... gave the name to this important branch of mathematics in the European world...” -Mohammad Kahn

17
Full name: Abu Ja’far Muhammad ibn Musa Al-Khwarizmi Lived 790-850 Of Persian descent May have been born in Baghdad or modern-day Uzbekistan

18
Wrote Algoritmi de numero Indorum (Al-Khwarizmi on the Hindu Art of Reckoning) Only words (no symbols or numerals) This text was later studied in Europe for centuries Studied quadratic equations and their solutions Invented “completing the square” and developed geometric representations of this process The terms algebra and algorithm come from his name.

19
Where was the center of wisdom and learning in the 9 th century? To what area of mathematics did Arabic mathematicians make the greatest contributions? Why is Al-Khwarizmi also called the Father of Algebra?

20
Goal is to manipulate an equation so that it can be factored nicely to solve for x Two methods 1)Al-Khwarizmi’s geometric representation 2)Algebraic representation

23
http://illuminations.nctm.org/ActivityDetail.aspx?I D=132

30
Work with your partner to complete the next 2 examples on your notes page. Be prepared to share with the class.

34
Partner on the left complete the square to solve for x: Partner on the right complete the square to solve for x: WHEN I SAY GO: Switch sticky notes with your partner and check their work. If you find a mistake, talk it out with them. When BOTH of you agree on BOTH problems, put your sticky notes on the board. Who can be the first pair to get the correct answer?? x 2 – 8x – 1 = 0 x 2 + 6x – 7 = 0

35
http://library.thinkquest.org/3526/facts/timeline.html http://library.thinkquest.org/3526/facts/timeline.html http://www-groups.dcs.st- and.ac.uk/~history/HistTopics/Arabic_mathematics.html http://www-groups.dcs.st- and.ac.uk/~history/HistTopics/Arabic_mathematics.html http://www.math.tamu.edu/~dallen/masters/islamic/arab.pdf http://www.math.tamu.edu/~dallen/masters/islamic/arab.pdf www.google.com/maps www.google.com/maps http://www.algebra.com/algebra/about/history/Al- Khwarizmi.wikipedia http://www.algebra.com/algebra/about/history/Al- Khwarizmi.wikipedia http://3.bp.blogspot.com/-LbVOcoKtCkI/TVl- 4IV3gLI/AAAAAAAAAAw/WUCQGD3JhLg/s1600/Algoritmi.jpg http://3.bp.blogspot.com/-LbVOcoKtCkI/TVl- 4IV3gLI/AAAAAAAAAAw/WUCQGD3JhLg/s1600/Algoritmi.jpg http://www.storyofmathematics.com/islamic_alkhwarizmi.html http://www.storyofmathematics.com/islamic_alkhwarizmi.html http://www.csames.illinois.edu/documents/outreach/Completin g_the_Square_Lesson_Plan.pdf http://www.csames.illinois.edu/documents/outreach/Completin g_the_Square_Lesson_Plan.pdf

Similar presentations

Presentation is loading. Please wait....

OK

Complex Numbers and Roots

Complex Numbers and Roots

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on advancing and retreating monsoon Ppt on organic led Ppt on network topologies and its types Free ppt on self esteem Download ppt on internet services for class 10 Cathode ray tube display ppt online Ppt on foundation in civil engineering Ppt on memory of computer Ppt on astronomy and astrophysics journals Ppt on 60 years of indian parliament members