Chapter 5.9 Complex Numbers Standard & Honors

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Presentation transcript:

Chapter 5.9 Complex Numbers Standard & Honors Algebra II Mr. Gilbert Chapter 5.9 Complex Numbers Standard & Honors 12/10/2018

Agenda Warm-up (next slide) Return Class work Lesson Homework Check your answers Return Class work Lesson Homework 12/10/2018

Class Work: Warm-up 7.9 (5 min.) Solve: 12/10/2018

Warm-up 7.9 (5 min.) Solve: 12/10/2018

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 12/10/2018 Lesson 9 Contents

12/10/2018

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. 12/10/2018

Simplify . Answer: 12/10/2018 Example 9-1a

Simplify . Answer: 12/10/2018 Example 9-1b

Simplify. a. b. Answer: Answer: 12/10/2018 Example 9-1c

Simplify . Answer: = 6 12/10/2018 Example 9-2a

Simplify . Answer: 12/10/2018 Example 9-2b

Simplify. a. b. Answer: –15 Answer: 12/10/2018 Example 9-2c

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

Simplify . Answer: i 12/10/2018 Example 9-3b

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: 12/10/2018 Example 9-4a

Solve Answer: 12/10/2018 Example 9-4b

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: 12/10/2018 Example 9-5a

Find the values of x and y that make the equation true. Answer: 12/10/2018 Example 9-5b

Commutative and Associative Properties Simplify . Commutative and Associative Properties Answer: 12/10/2018 Example 9-6a

Commutative and Associative Properties Simplify . Commutative and Associative Properties Answer: 12/10/2018 Example 9-6b

Simplify. a. b. Answer: Answer: 12/10/2018 Example 9-6c

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 1 + 4 j amps and impedance 3 – 6 j ohms. Electricity formula FOIL Multiply. Add. Answer: The voltage is volts. 12/10/2018 Example 9-7a

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 3 + 2 j ohms. Answer: 9 – 7 j 12/10/2018 Example 9-7b

Simplify . and are conjugates. Multiply. Answer: Standard form 12/10/2018 Example 9-8a

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

Simplify. a. b. Answer: Answer: 12/10/2018 Example 9-8c

Homework Review 12/10/2018

Homework See Syllabus 5.9 page 274: 18 - 60 multiples of 3, 62-65. 12/10/2018

Homework - Honors See Syllabus 5.9 page 274: 18 - 60 multiples of 3, 62-65. 12/10/2018

End of Custom Shows WARNING! Do Not Remove This slide is intentionally blank and is set to auto-advance to end custom shows and return to the main presentation. 12/10/2018 End of Custom Show