Algebra 2 4-8 Guided Practice: Complex Numbers

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Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It! Here is a partially-completed multiplication table. Use the following information to complete the table using only the values a, b, c, & d. 

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For these items, enter only a, b, c, or d.

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Recall the real number families, shown in this diagram from Chapter 1

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Take Note: Define the imaginary unit i.

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Take Note: Fill in the blank with the numeric value of i.

i =_____

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Take Note: Describe the process of rewriting the square root of a negative number.

NOTE: This is a free response Formative item. A variety of media options are available for use in your response.

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Problem 1 Got It? How do you write the number by using the imaginary unit i ?

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Problem 1 Got It? How do you write the number by using the imaginary unit i ?

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Problem 1 Got It? How do you write the number by using the imaginary unit i ?

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Problem 1 Got It? Reasoning: Explain why the two radicals below are not equivalent.

You may use the canvas to help illustrate your written response.

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Define complex number.

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Take Note: Provide an example of a complex number.

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Take Note: Define pure imaginary number.

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Take Note: Provide an example of a pure imaginary number.

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Take Note: Describe the complex plane.
How is it similar to the standard coordinate plane? How is it different?
You may use the canvas to help illustrate your explanation.

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Take Note: Define the absolute value of a complex number. You may use the canvas to help illustrate your written response.

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Take Note: Use the math input keyboard to complete this equation representing the absolute value of a complex number.
|a+bi|=_____

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Problem 2 Got It? Graph the complex numbers on the complex plane. Use the color indicated for each number. Include relevant graph detail: label axes, and indicate units and scale on both axes.

5 - i
-3 - 2i
1 + 4i

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Problem 2 Got It? Match each complex number with its absolute value.

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Take Note: Summarize the processes for adding and subtracting complex numbers.

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Problem 3 Got It? Evaluate the expression below.

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Problem 3 Got It?

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Problem 3 Got It?

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Problem 3 Got It?

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Take Note: Summarize the process for multiplying complex numbers. How is it the same as multiplying binomials? How is it different?

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Problem 4 Got It?

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Problem 4 Got It?

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Problem 4 Got It?

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Define complex conjugates.

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Take Note: What is the complex conjugate of 4+5i?

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Take Note: What do you know about the product of 2 complex conjugates? You may use the canvas to help illustrate your written response.

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Problem 5 Got It?

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Problem 5 Got It?

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Problem 5 Got It?

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Problem 6 Got It?

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Problem 6 Got It?

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Problem 7 Got It?

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Problem 7 Got It?

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Video Check: Select all that apply with regards to the video embedded directly above this item.

For these items, enter only a, b, c, or d.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Define the imaginary unit i.

Take Note: Fill in the blank with the numeric value of i.i =_____

Take Note: Describe the process of rewriting the square root of a negative number.NOTE: This is a free response Formative item. A variety of media options are available for use in your response.

Problem 1 Got It? How do you write the number by using the imaginary unit i ?

Problem 1 Got It? How do you write the number by using the imaginary unit i ?

Problem 1 Got It? How do you write the number by using the imaginary unit i ?

Problem 1 Got It? Reasoning: Explain why the two radicals below are not equivalent. You may use the canvas to help illustrate your written response.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Define complex number.

Take Note: Provide an example of a complex number.

Take Note: Define pure imaginary number.

Take Note: Provide an example of a pure imaginary number.

Take Note: Describe the complex plane. How is it similar to the standard coordinate plane? How is it different?You may use the canvas to help illustrate your explanation.

Take Note: Define the absolute value of a complex number. You may use the canvas to help illustrate your written response.

Take Note: Use the math input keyboard to complete this equation representing the absolute value of a complex number. |a+bi|=_____

Problem 2 Got It? Graph the complex numbers on the complex plane. Use the color indicated for each number. Include relevant graph detail: label axes, and indicate units and scale on both axes.5 - i-3 - 2i1 + 4i

Problem 2 Got It? Match each complex number with its absolute value.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the processes for adding and subtracting complex numbers.

Problem 3 Got It? Evaluate the expression below.

Problem 3 Got It?

Problem 3 Got It?

Problem 3 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the process for multiplying complex numbers. How is it the same as multiplying binomials? How is it different?

Problem 4 Got It?

Problem 4 Got It?

Problem 4 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Define complex conjugates.

Take Note: What is the complex conjugate of 4+5i?

Take Note: What do you know about the product of 2 complex conjugates? You may use the canvas to help illustrate your written response.

Problem 5 Got It?

Problem 5 Got It?

Problem 5 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 6 Got It?

Problem 6 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 7 Got It?

Problem 7 Got It?

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note: Fill in the blank with the numeric value of i.

i =_____

Take Note: Describe the process of rewriting the square root of a negative number.

NOTE: This is a free response Formative item. A variety of media options are available for use in your response.

Problem 1 Got It? Reasoning: Explain why the two radicals below are not equivalent.

You may use the canvas to help illustrate your written response.

Take Note: Describe the complex plane.
How is it similar to the standard coordinate plane? How is it different?
You may use the canvas to help illustrate your explanation.

Take Note: Use the math input keyboard to complete this equation representing the absolute value of a complex number.
|a+bi|=_____

Problem 2 Got It? Graph the complex numbers on the complex plane. Use the color indicated for each number. Include relevant graph detail: label axes, and indicate units and scale on both axes.

5 - i
-3 - 2i
1 + 4i

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?