Quadratics

Lesson 8

Math

Unit 2

11th Grade

Lesson 8 of 11

Objective


Add, subtract, and multiply complex numbers.

Common Core Standards


Core Standards

  • N.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.
  • N.CN.A.2 — Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Foundational Standards

  • N.RN.B.3

Criteria for Success


  • Use the commutative, associative, and distributive properties to rewrite expressions with complex numbers.
  • Write imaginary parts of complex numbers appropriately, representing $${i^2}$$ as $${-1}$$ and combining terms as needed. 
  • Describe that the value of $$i$$ is constant, and while it does not have a real approximation, it is not a variable.
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Anchor Problems


Problem 1

This is a complex number because it has a real part and an imaginary part:

$${{3+2i}}$$

What is the sum of $${{3+2i}}$$ and $${2+4i}$$?

Guiding Questions

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Problem 2

What is the product of $${(3+2i)}$$ and $${(2+4i)}$$?

Guiding Questions

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Target Task


Problem 1

Evaluate the following complex expressions:

$${(8+3i)-(6-2i)}$$

$${(8+3i)(6-2i)}$$

$${(2+i)^2+(6+2i)}$$

Problem 2

Which of the following results in a real number? Select all that apply.

$${i^2}$$

$${(2-i)(2+i)}$$

$${2i^3}$$

$${3i+2i}$$

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems where students need to identify values of expressions that result in real numbers. 
  • Include problems that require students to identify complex roots via the quadratic formula.
  • Include problems such as “Determine whether this statement is always, sometimes, or never true: ‘The sum of two complex numbers is real.’ Explain your reasoning."
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Lesson 7

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Lesson 9

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Features of Quadratic Functions

Topic B: Imaginary Solutions and Operating with Complex Numbers

Topic C: Applications, Systems, and Inverse with Quadratics

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