Complex Numbers

CCSS objective: Use complex numbers in polynomial identities  N-CN.1 Know there is a complex number i such that i 2 = −1, and every complex number has the form a + bi with a and b real.  N-CN.2 Use the relation i 2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Monday & Tuesday Monday: (all) new material  CTA: All of class do slides, video and worksheet; – 2-5 Complex Number part 1 Tuesday: (all) new material  CTA *Enrichment do next level with video & discussion; 2-5 Complex Number Video part 4 Point out during video, play twice: ask students first, don’t just give answer: x2 – 12x + 48 = 36 turns into Vertex Form *Non-enrichment, poster textbook p. 275

Imaginary Numbers: where i is the imaginary unit i is not a variable it is a symbol for a specific number

Simplify each expression. 2. √ √ √-81 = √100 √-1 = √81 √-1 =

Remember Simplify each expression. 6. 4i ∙ 3i 7. 19i ∙ 17i = = 12i 2 Leave space in your notes for #5 = 12 ∙ -1

Do separately ? Must combine first ? 8. √-100 ∙ √-81 =

Application: Imaginary Numbers  Monday: (all students) textbook p. 278, even only, # 2-10 & even only, 42-46; copy problem & circle your answer to be graded.  Do at the beginning of next class

Teaching note: Tuesday *Non-Enrichment: in teams of no more than 3, make poster of number chart on p. 275 of textbook. You will be graded based on effort, do = 100% *Enrichment do next level with video & discussion; 2-5 Complex Number Video part 4 Point out during video, play twice: ask students first, don’t just give answer: x2 – 12x + 48 = 36 turns into Vertex Form

Simplify: Enrichment To figure out where we are in the “i”cycle divide the exponent by 4 and look at the remainder.

Simplify:Enrichment Divide the exponent by 4 and look at the remainder.

Teaching note: Thursday Lesson Tutorial Video: 2-9 Operations with Complex Numbers part 5 Imaginary with Distribution & FOIL

Definition of Equal Complex Numbers Two complex numbers are equal if their real parts are equal and their imaginary parts are equal. If a + bi = c + di, then a = c and b = d

Simplify: When adding or subtracting complex numbers, combine like terms.

Simplify.

9 – 6i -12 – 2i

Application  Textbook p. 278 #29-34 –Non-Enrichment: p.278 #50-52 –Enrichment: p/ 278 #14-16 l Must show work up to point of calculator entry l Must write question l Circle answer you want graded  Due next class

Friday

Multiplying Complex Numbers. To multiply complex numbers, you use the same procedure as multiplying polynomials. F O I L

Multiplying: (a + b)(c + d) Multiplying Polynomials  (a + b)(c + d)  (a – b)(c – d)  (a + b)(c – d) Multiplying Complex Numbers  (a + bi)(c + di)  (a – bi)(c – di)  (a + bi)(c – di)

Simplify. F O I L 16 – 24i + 10i -15(-1)

Simplify. F O I L

Group work  Teams of no more than 2; both names on one paper if fine. Everyone in team must understand how to do if asked.  look up and define the vocabulary term Conjugate  Textbook page 279 # l Due next classhint: Order of Operations l Circle answer l Write question