1. Chapter 5.9 Complex Numbers Standard & Honors
Algebra II Mr. Gilbert
Chapter 5.9 Complex Numbers
Standard & Honors
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2. Agenda Warm-up (next slide) Return Class work Lesson Homework
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Lesson
Homework
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3. Class Work: Warm-up 7.9 (5 min.)
Solve:
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4. Warm-up 7.9 (5 min.)
Solve:
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5. Chapter 5.9 Complex Numbers
Example 1 Square Roots of Negative Numbers
Example 2 Multiply Pure Imaginary Numbers
Example 3 Simplify a Power of i
Example 4 Equation with Imaginary Solutions
Example 5 Equate Complex Numbers
Example 6 Add and Subtract Complex Numbers
Example 7 Multiply Complex Numbers
Example 8 Divide Complex Numbers
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Lesson 9 Contents

6. 12/10/2018

7. Complex Numbers COMPLEX NUMBERS:
Definitions:
The “imaginary” number i where
COMPLEX NUMBERS:
Have 2 parts, a real part and an imaginary part.
Written a+bi
where a is the real part
and bi is the imaginary.
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8. Simplify .
Answer:
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Example 9-1a

9. Simplify .
Answer:
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Example 9-1b

10. Simplify. a. b.
Answer:
Answer:
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Example 9-1c

11. Simplify .
Answer: = 6
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Example 9-2a

12. Simplify .
Answer:
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Example 9-2b

13. Simplify. a. b.
Answer: –15
Answer:
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Example 9-2c

14. Simplify Multiplying powers Power of a Power Answer: 12/10/2018
Example 9-3a

15. Simplify .
Answer: i
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Example 9-3b

16. Subtract 20 from each side.
Solve
Original equation
Subtract 20 from each side.
Divide each side by 5.
Take the square root of each side.
Answer:
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Example 9-4a

17. Solve
Answer:
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Example 9-4b

18. Find the values of x and y that make the equation true.
Set the real parts equal to each other and the imaginary parts equal to each other.
Real parts
Divide each side by 2.
Imaginary parts
Answer:
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Example 9-5a

19. Find the values of x and y that make the equation true.
Answer:
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Example 9-5b

20. Commutative and Associative Properties
Simplify .
Commutative and Associative Properties
Answer:
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Example 9-6a

21. Commutative and Associative Properties
Simplify .
Commutative and Associative Properties
Answer:
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Example 9-6b

22. Simplify. a. b.
Answer:
Answer:
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Example 9-6c

23. Answer: The voltage is volts.
Electricity In an AC circuit, the voltage E, current I, and impedance Z are related by the formula Find the voltage in a circuit with current j amps and impedance 3 – 6 j ohms.
Electricity formula
FOIL
Multiply.
Add.
Answer: The voltage is volts.
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Example 9-7a

24. Electricity In an AC circuit, the voltage E, current I, and impedance Z are related by the formula E = I • Z. Find the voltage in a circuit with current 1 – 3 j amps and impedance j ohms.
Answer: 9 – 7 j
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Example 9-7b

25. Simplify . and are conjugates. Multiply. Answer: Standard form
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Example 9-8a

26. Simplify . Multiply by Multiply. Answer: Standard form 12/10/2018
Example 9-8b

27. Simplify. a. b.
Answer:
Answer:
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Example 9-8c

28. Homework Review
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29. Homework See Syllabus 5.9 page 274: 18 - 60 multiples of 3, 62-65.
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30. Homework - Honors See Syllabus 5.9
page 274: multiples of 3,
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