3.9 Complex Numbers (Division)

3.9 Complex Numbers (Division)

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Unit 3: Polynomials

Vocabulary-

Complex Conjugate-

Every complex number has a complex conjugate that is used in division. You find the complex conjugate by switching the sign of the imaginary number.

Example: 3-2i and 3+2i are complex conjugates.

Multiple Choice

What is the complex conjugate of  4 - 3i?

• A.  1/(4-3i)

• B. 1/(4+3i)

• C.  -4 + 3i

• D.  4 + 3i

Multiple Choice

What is the conjugate of -2i + 7

• -2i - 7

• 2i - 7

• -7 + 2i

• 7 + 2i

Multiple Choice

What is the conjugate of -2i + 7

• -2i - 7

• 2i - 7

• -7 + 2i

• 7 + 2i

Multiplying Conjugates

Some text here about the topic of discussion

​Multiplying complex conjugates always result in a real number.

Ex. (3-i)(3+i)

Multiple Choice

Multiply: (4 - i)(4 + i)

• $$16-i^2$$

• 17

• $$16-8i-i^2$$

• 17-8i

Multiple Choice

Multiply (5 + 2i)(5 - 2i)

• $$25-i^2$$

• 21

• 29

• 29-10i

Multiple Choice

Multiply (6 - 2i)(6 + 2i)

• 40

• 32

• $$36-i^2$$

• 36-12i

Multiple Choice

What type of number is the result of multiplying a complex number and its conjugate?

• Natural Number

• Imaginary Number

• Irrational Number

• Real Number

Dividing Complex Numbers

Steps:

1. Find the complex conjugate of the denominator.

2. Multiply the top and bottom of the fraction by the complex conjugate

3. Simplify the fraction

Multiple Choice

• A

• B

• C

• D

Multiple Choice

What is the simplified form of the above?

• $$\frac{7+11i}{10}$$  

• $$\frac{13+i}{10}$$  

• $$\frac{5-3i}{2}$$  

• $$\frac{7-11i}{10}$$  

Multiple Choice

Simplify

• (-10+6i)/17

• (1+50i)/61

• (-23+36i)/25

• (-21+33i)/34