Operations with Complex Numbers

TIME FRAME: 2 days PREREQUISITE SKILLS  Simplify radicals Unit 4:Operations Concept 4 with Complex Numbers  Perform operations with pure imaginary numbers  Multiply polynomials Operations Perform operations with with Complex complex numbers Numbers  HONORS ONLY:

ACHIEVE , INC. STANDARD CORE LEARNING GOAL INDICATOR Algebra 2. O2.b Perform operations on Indicator 2.7.2 The student will perform operations on complex numbers. the set of complex numbers SKILLS STATEMENTS: The student will represent the square root of a negative number in the form bi, where b is real; simplify powers of pure imaginary numbers. The student will add, subtract, and multiply complex numbers. s

l The student will simplify rational expressions containing complex numbers in the

l denominator i

k VOCABULARY ENDURING UNDERSTANDINGS

S Imaginary unit  Complex number written in standard from is a number a+bi where a and b are real Imaginary number numbers. The number a is the real part of the complex number. The number bi is the

d Pure imaginary numbers imaginary part.

n Complex numbers  Complex conjugates-Two complex numbers of the form a+bi and a-bi are called

a Complex conjugates complex conjugates. Real numbers  The product of complex conjugates is always a real number.

e Add  Pure imaginary and real numbers are both subsets of the set of complex numbers.

g Subtract

d Multiply ESSENTIAL QUESTIONS

e Divide  How do you perform operations on complex numbers? l  Find the value of x, in the equation x2 = -5.

w  How do you express, -3i(5-2i) as a complex number in standard form?

o  What is the difference between an imaginary number and an imaginary unit? n CONCEPT KNOWLEDGE AND PROCESS K  The imaginary unit i is defined to be, . Then,

 To add or subtract complex numbers, add/subtract their real parts and their imaginary parts separately.  To multiply two complex numbers, use the distributive property or the FOIL method.  Numbers of the form 7i, 20i and i 8 are called pure imaginary numbers. Baltimore City Public Schools Algebra 2 Math Curriculum DRAFT Office of Math: [email protected] Page 1 Unit 4: Concept 4 Operations with Complex Numbers

Baltimore City Public Schools Algebra 2 Math Curriculum DRAFT Office of Math: [email protected] Page 2 Unit 4: Concept 4 Operations with Complex Numbers

d RESOURCES e Sub-Skills Glencoe- Algebra 2 McDougal-Littell- McDougal-Littell- Other Resources n t ERROR IDENTIFICATION Glencoe- Algebra 2 McDougal-Littell- McDougal-Littell- Algebra 2: Algebra 2: MD Edition (teacher-made, o s Algebra 2: Concept Algebra 2: MD i Concept & Skills websites,etc.) t e & Skills Edition

n Perform  Check your ● na  TE & SE pp. 275-282  Purplemath g Perform operations with pure  pp.276-277  na  pp. 276-279 e operations Understanding p.280  Teaching  Coolmath g v with pureimaginary Items numbers 1-6 Guide/Lesson Plan pp. r u imaginaryIF students have Practice THEN and consider Problem  TE pp.276-27765-66  TE pp. 276-277 e S t numberstrouble with Solving p. 280reminding Items them to Examples 1-3 Practice levels A, B, C Extra Examples 2 n

n imaginary 18-25 perform the  TE p.277 Additionalpp. 67-69 & 4 I a operations Study guideoperations and like Examples 1-3Study Guide pp. 70-  TE pp. 278-279  l r Interventionpolynomials, pp. 24-25 but 71 Extra Examples 5 P o  Higher Orderthe Thinking imaginary unit & 7

r  SE pp. 276-279 r Problems p.i 281must #66 be g

E Perform  Check your simplified. Like● Guided Practice  TE & SE pp. 275-282  AlgebraLabExamples 2-7 n operations Understandingwhen p. you280 got 8ipp.264-2666,  Teaching  Purplemath i with complex Items 9-17this equal to 8(-● Quiz 2 p.266 Guide/Lesson Plan pp.  COMPLEXnumbers n numbers  Practice and1)=-8, Problem since Items 22-30 65-66  Regentsprep r Solving p. 280i6 =-1. Items  Catch-up for Absent  Online Practice a 26-35 More info. Students p. 72 e  Word Problem Practice  Application p. 73 L Perform operationsp. 28 with complex  pp.278-279 Challenge p.pp.261-263 74  pp. 276-279 numbers  Higher Order Thinking IF students are ProblemsTHEN p. remind281 Items them to  TE pp.278-279  TE pp.261-263  TE pp. 276-277 having 67-70 add/subtract the Examples 4-7 Examples 1-5 Extra Examples 2 TRACKINGproblems SHEET real partsCONCEPT and the  TE pp.278-279 HONORS Extra ExamplesOTHER WAYS& 4 TO operating with imaginaryASSESSMENT parts Additional RESOURCESpp.262-263 ASSESS TE pp. 278-279 complex separately. And to Examples 4-7 Extra Examples 5 numbers multiply, use FOIL & 7 method or  SE pp. 276-279 distributive. Examples 2-7 Several exercises Baltimore City Public Schools should be Algebra 2 Math Curriculum DRAFT Office of Math: [email protected] to them for Pagemastery. 3 Unit 4: Concept 4 Operations with Complex Numbers

Baltimore City Public Schools Algebra 2 Math Curriculum DRAFT Office of Math: [email protected] Page 4