Mini-Lecture 9.4: Complex Solutions of Quadratic Equations - Edubirdie

University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

454

Pages:

1
Author:

Macy Harrison

Mini-Lecture 9.4 Complex Solutions of Quadratic Equations Learning Objectives: 1. 2. 3. 4. 5. Write complex numbers using i notation. Add and subtract complex numbers. Multiply complex numbers. Divide complex numbers. Solve quadratic equations that have complex solutions. Examples: 1. Simplify each of the following using a) −49 b) −1 = i . −12 c) −80 2. Add or subtract as indicated. a) (3 − i ) + (5 + 4i ) b) (2 + 5i ) − (3 + 2i ) c) Subtract (8 − i ) from (3 + 4i ) b) (5 − 2i )(3 + i ) c) (1 + 2i )(1 − 2i ) 3. Multiply complex numbers. a) 2i(4-8i) 4. Divide complex numbers. a) 9 − 12i 3 b) 20 + 5i 5i c) 6−i 3 − 2i 5. Solve the following quadratic equations for complex solutions. a) ( x + 2) 2 = − 16 b) ( 3 x − 5 ) = −12 2 c) x 2 + 8 x + 20 = 0 Teaching Notes: • • • • • Remind students i 2 = −1 and i = −1 . Complex numbers can be written in the form a + bi. Complex numbers written in the form 0+ bi b ≠ 0 is also called a pure imaginary number. Complex number written in the form a + bi is in standard form. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 7i; 1b) 2i 3 ; 1c) 4i 5 ; 2a) 8 + 3i; 2b) -9 + 3i; 2c) -5 + 5i; 3a) 16 + 8i; 3b) 17 - i; 3c) 5; 4a) 3 – 4i; 4b) 5± 2 3 20 + 9i ; 4c) 1 – 4i; 5a) 2 ± 4i ; 5b) ; 5c) −4 ± 2i 3 14

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