Exploring Operations with Complex Numbers

This video lesson explores imaginary and complex numbers, focusing on their applications in engineering, electric circuits, and fluid dynamics. It explains the components of complex numbers and demonstrates operations like addition, subtraction, and multiplication. The lesson includes example problems and a challenge problem involving a quadratic equation to reinforce understanding.

Which of the following is an application of complex numbers?

• Finding the volume of a sphere

• Calculating the area of a triangle

• Studying the flow of fluid around objects

• Determining the speed of light

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CCSS.HSN.CN.A.1

In the complex number 4 - 10i, what is the imaginary part?

• -10

• 4

• -10i

• 4i

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CCSS.HSN.CN.A.1

What is the real part of the complex number 0 + 12i?

• None

• 12i

• 12

• 0

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CCSS.HSN.CN.A.2

When adding 5 + 2i and 3 + 4i, what is the result?

• 2 + 8i

• 8 + 6i

• 8 + 2i

• 5 + 6i

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CCSS.HSN.CN.A.2

What is the result of subtracting 7 - 8 from 6i - (-5i)?

• -1 + 11i

• -1 - 11i

• 1 + 11i

• 1 - 11i

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CCSS.HSN.CN.A.2

What is the product of 5 and 4 in the context of complex numbers?

• 24i

• 9

• 20

• 15i

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CCSS.HSN.CN.A.2

In the multiplication of complex numbers, what does i squared equal?

• 0

• i

• -1

• 1

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CCSS.HSN.CN.A.2

What is the result of multiplying 3 + i by 3 + i?

• 9 + 6i - 1

• 9 + 6i + 1

• 9 - 6i - 1

• 9 - 6i + 1

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CCSS.HSN.CN.C.8

What is the simplified form of 3 + i quantity squared?

• 8 + 6i

• 9 + 6i

• 8 - 6i

• 9 - 6i

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CCSS.HSN.CN.C.9

Is 3 + i a solution to the quadratic equation x^2 - 6x + 10 = 0?

• No, because it does not satisfy the equation

• Yes, because it satisfies the equation

• No, because it is not a real number

• Yes, because it is a complex number

Tags

CCSS.HSN.CN.C.9