Intermediate Algebra – Student Workbook – Second Edition 2013

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

Lesson 5b - Solving Quadratic Equations Mini-Lesson Problem 9 WORKED EXAMPLE – OPERATIONS WITH COMPLEX NUMBERS Simplify each of the following and write in the form a + bi a) 16 1 16 b) Note: This is SUBTRACTION and not FOIL. 4 1 (3 2i) (4 i) 3 2i 4 i 0 4i 1 3i c) (2 i)(4 2i) 8 4i 4i 2i 8 2i 2 8 2( 1) 8 2 10 0i 2 Note: This one is FOIL. You can also just enter (2 + i)(4 – 2i) on your calculator if you put your calculator in a + bi mode. To work with i on your calculator, press MODE then change REAL to a+bi by using your arrow keys. The i button is on the bottom row. Problem 10 MEDIA EXAMPLE – OPERATIONS WITH COMPLEX NUMBERS Simplify each of the following and write in the form a + bi. To work with i on your calculator, press MODE then change REAL to a+bi by using your arrow keys. The i button is on the bottom row. a) (2 – 3i) – (4 + 2i) = b) 4i(5 – 2i) = c) (2 – i)(1 + i) = Scottsdale Community College Page 224 Intermediate Algebra
Lesson 5b - Solving Quadratic Equations Mini-Lesson Work through the following to see how to deal with equations that can only be solved in the Complex Number System. Problem 11 WORKED EXAMPLE – SOLVING QUADRATIC EQUATIONS WITH COMPLEX SOLUTIONS Solve 2x 2 + x + 1= 0 for x. Leave results in the form of a complex number, a+bi. First, graph the two equations as Y1 and Y2 in your calculator and view the number of times the graph crosses the x-axis. The graph below shows that the graph of y = 2x 2 + x + 1 does not cross the x-axis at all. This is an example of our Case 3 possibility and will result in no Real Number solutions but two unique Complex Number Solutions. To find the solutions, make sure the equation is in standard form (check). Identify the coefficients a = 2, b = 1, c = 1. Insert these into the quadratic formula and simplify as follows: 2 1 1 4(2)(1) 1 18 1 7 x 2(2) 4 4 Break this into two solutions and use the a+bi form to get x 1 1 7 4 1 4 1 i 4 1 4 7 4 7 4 7 4 i and x 2 1 7 4 1 4 1 i 4 1 4 7 4 7 4 7 4 i The final solutions are x 1 4 7 i, x 4 1 4 1 2 7 i 4 Remember that 1 i so 7 i 7 Scottsdale Community College Page 225 Intermediate Algebra
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Scottsdale Community College Interm
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Table of Contents Lesson 1a - Intro
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Lesson 1a - Introduction to Functio
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Lesson 1b - Linear Equations In the
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Lesson 1b - Linear Equations Mini-L
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Lesson 4b - More on Logarithms This
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Lesson 4b - More on Logarithms Mini
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Lesson 6b - Rational Exponents and
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Appendix A: You Try Answers Lesson
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Appendix A: You Try Answers You Try
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Intermediate Algebra – Student Workbook – Second Edition 2013

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