#  p. 99 only (for now) (3i)(4i) i(2i)(-4i) √-10 ∙ √-15 YOU MUST TAKE OUT THE i FIRST!!!

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 p. 99 only (for now)

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

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

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

5x 2 = -125

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

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

(3 – 2i) – (6 + 3i)

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

(5 + i)(5 – i)

 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

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

Honors Algebra II

 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 )

“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

 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

 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.

 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?

 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

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

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

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

 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

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