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Use properties to multiply complex numbers in the form of a + bi with a and b being real numbers.
Clarifications:

Essential Understandings

Concrete:

  • Match i with the  begin mathsize 12px style square root of negative 1 end root end style.

    Table showing Powers of i with their simplified imaginary numbers.
  • Match the parts of a complex number with a label.
    e.g., a + bi (a is the real part and bi is the imaginary part)
    i =  begin mathsize 12px style square root of negative 1 end root end style.
  • Use manipulatives to represent terms for the purpose of simplifying and combining like terms.
  • Use manipulatives to combine like terms (i.e., demonstrate 5i + 3i by combining like manipulatives).
  • Create an array of objects for the mathematical equation and match the answer symbol (+ or -) following addition/subtraction rules for an equation.
  • Create an array of objects for the mathematical equation and match the sign positive or negative following multiplication rules for an equation. 
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Representation:
  • Understand the following concepts, symbols, and vocabulary for: like terms, combine, variables, positive integer, negative integer, real number, imaginary number, complex number, squares, square roots.
  • Understand that i in its simplified form changes its sign based on its exponent. For example:
    Table showing Powers of i with their simplified imaginary numbers.
  • Use tools, as needed, to multiply two complex numbers.
    For example:
    Reminder: i²  = -1
    (a + bi)(c + di) = ac + adi + bci + bdi²

    (2 + 3i)(1 + 2i) = 2 + 4i + 3i + 6i² 

    2 + 7i – 6 = -4 + 7i

Access Point #: MAFS.912.N-CN.1.AP.2b (Archived Access Point)
Access Point Standards

Visit the specific benchmark webpage to find related instructional resources.

  • MAFS.912.N-CN.1.2: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
Access Point Information
Number:
MAFS.912.N-CN.1.AP.2b
Category:
Access Points
Date Adopted or Revised:
06/14
Cluster:
Perform arithmetic operations with complex numbers. (Algebra 2 - Additional Cluster) : 

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Access Point Courses
  • Algebra 2 (#1200330): In Algebra 2, instructional time will emphasize five areas: (1) extending arithmetic operations with algebraic expressions to include radical and rational expressions and polynomial division; (2) graphing and analyzing functions including polynomials, absolute value, radical, rational, exponential and logarithmic; (3) building functions using compositions, inverses and transformations; (4) extending systems of equations and inequalities to include non-linear expressions and (5) developing understanding of the complex number system, including complex numbers as roots of polynomial equations.

    All clarifications stated, whether general or specific to Algebra 2, are expectations for instruction of that benchmark

    Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.

  • Algebra 2 Honors (#1200340): In Algebra 2 Honors, instructional time will emphasize six areas: (1) developing understanding of the complex number system, including complex numbers as roots of polynomial equations; (2) extending arithmetic operations with algebraic expressions to include polynomial division, radical and rational expressions; (3) graphing and analyzing functions including polynomials, absolute value, radical, rational, exponential and logarithmic; (4) extending systems of equations and inequalities to include non-linear expressions; (5)building functions using compositions, inverses and transformations and (6) developing understanding of probability concepts.

    All clarifications stated, whether general or specific to Algebra 2 Honors, are expectations for instruction of that benchmark.

    Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.

  • Liberal Arts Mathematics (#1207310):
  • Analytic Geometry (#1206330):
  • Algebra 2 for Credit Recovery (#1200335): Special notes: Credit Recovery courses are credit bearing courses with specific content requirements defined by Next Generation Sunshine State Standards and/or Florida Standards. Students enrolled in a Credit Recovery course must have previously attempted the corresponding course (and/or End-of-Course assessment) since the course requirements for the Credit Recovery course are exactly the same as the previously attempted corresponding course. For example, Geometry (1206310) and Geometry for Credit Recovery (1206315) have identical content requirements. It is important to note that Credit Recovery courses are not bound by Section 1003.436(1)(a), Florida Statutes, requiring a minimum of 135 hours of bona fide instruction (120 hours in a school/district implementing block scheduling) in a designed course of study that contains student performance standards, since the students have previously attempted successful completion of the corresponding course. Additionally, Credit Recovery courses should ONLY be used for credit recovery, grade forgiveness, or remediation for students needing to prepare for an End-of-Course assessment retake.
  • Access Algebra 2 (#7912095):
    Access Courses:

    Access courses are for students with the most significant cognitive disabilities. Access courses are designed to provide students access to grade-level general curriculum. Access points are alternate academic achievement standards included in access courses that target the salient content of Florida’s standards. Access points are intentionally designed to academically challenge students with the most significant cognitive disabilities.