HSN.CN.A.1: Perform Arithmetic Operations with Complex Numbers

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Addressed CCSS for Mathematics:

CCSS.MATH.CONTENT.HSN.CN.A.1
Know there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real.

CCSS.MATH.CONTENT.HSN.CN.A.2
Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

CCSS.MATH.CONTENT.HSN.CN.A.3
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Addressed Mathematical Practices:

CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

Learning Progression Overview:

The lesson will open up with a brief recap to refresh the students on the prerequisite knowledge that is required. After this, the instructor is to present the concept of an imaginary number. The presentation follows the same format as described in the textbook, “Algebra 2”. To put imaginary numbers into context, the instructor will provide a quadratic equation, such that an imaginary number is produced, for the students to solve. Upon deriving the complex number, the instructor will introduce the properties of the imaginary number, i and complex numbers. The students will then transition into their first entry task of performing operations in complex numbers, beginning with addition and subtraction. Succeeding this, the students will learn proceed to their second entry task of multiplying complex numbers, employing their knowledge of the distributive property.  The third entry task will center on the utilization of the conjugate to simplify instances of a number being divided by a complex number. Throughout, the instructor is to prompt the class with short “checks” in the form of verbal questions to assess the progress of the class. Finally, the students will be administered an assessment to gauge their overall mastery of the material. The learning progression can viewed at the link below.

Complex Numbers Learning Progression

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