Conjugates and Dividing Imaginary Numbers

Algebra 2

Unit 2, Lesson 7

Dividing Complex
Numbers

Volume 1, pg. 105

Drag and Drop

Bellwork:

Simplify each expressions.

a) 3i(-5)​

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b) 10i-3i​

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c) 4i(-4i)​

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d) -3i-7i​

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e) -4i-8i​

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Drag these tiles and drop them in the correct blank above

-15i

7i

16

-10i

-12i

16i

15i

10i

12i

-16

Learning Goals:

volume 1, pg. 105

The students will be able to:

 divide complex numbers.

volume 1, pg. 105

​Explain why your solution can be described this way.   Two complex numbers that have the same real part and opposite imaginary parts are known as complex conjugates. Complex conjugates are two complex numbers written in the form 𝒂+𝒃𝒊 and 𝒂−𝒃𝒊.

​

volume 1, pg. 105

​Explain why your solution can be described this way.   Two complex numbers that have the same real part and opposite imaginary parts are known as complex conjugates. Complex conjugates are two complex numbers written in the form 𝒂+𝒃𝒊 and 𝒂−𝒃𝒊.

​

volume 1, pg. 105

volume 1, pg. 105

volume 1, pg. 105

volume 1, pg. 105

Multiple Choice

Use complex conjugate to find the quotient of the complex expressions.

$$\frac{5}{1+i}$$

• $$\frac{5-5i}{2}$$

•  $$\frac{5+5i}{2}$$

• 5 - 5i
•  $$\frac{5-5i}{2i}$$

Multiple Choice

Use complex conjugate to find the quotient of the complex expressions.

$$\frac{3-3i}{4i}$$

• $$\frac{-3-3i}{4}$$

•  $$\frac{3+3i}{4}$$

• 3 - 3i

•  $$\frac{3-3i}{4i}$$

Multiple Choice

Use complex conjugate to find the quotient of the complex expressions.

$$\frac{4+4i}{2-9i}$$

• $$\frac{-28+44i}{85}$$

•  $$\frac{-28-44i}{4}$$

• -28+44i

•  $$\frac{-28-44i}{85}$$

Multiple Choice

Use complex conjugate to find the quotient of the complex expressions.

$$\frac{8+i}{i-2}$$

• $$\frac{-3-2i}{5}$$

•  $$\frac{-3+2i}{-5}$$

• -3-2i

•  $$-3+2i$$