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The Complex Number System Name: ____TEACHER COPY ______ _______ CCSS.Math.Content.HSN.CN.C.7 Date: ______________________ Period: _____ Solve quadratic equations with real coefficients that have complex solutions. Lesson Plan: 1. Hook: Radical Sign: I love you! So why can't we be together? Complex Number: It's complex. 2. Introduction and Vocabulary: In order to understand and simplify complex numbers, we need to first discuss some vocabulary used with them: real numbers, coefficients, radical sign, square root, commutative, associative, distributive, binomial, trinomial, factor, imaginary numbers and complex numbers. 3. Guided Practice / Review: After the vocabulary review, students simplify the following problems on their own: A. i2 B. i7 C. i14 D. i17 Next, they plot the following complex numbers on the complex plane: A. 2i B. 3 + 2i C. -1 + 2i D. 3 - 2i Simplify the following expressions. A. (1 + 8i) + (2 – 3i) B. (1 + 8i) - (2 – 3i) C. (1 + 8i)(2 – 3i) Check student work and review any discrepancies. 4. Independent Practice : Students will review the quadratic formula and discriminants and apply them in problems that involve complex number solutions. After reviewing as a group, have the students work independently on the specific examples. At this point, I chose not to address the Fundamental Theorem of Algebra yet. If you choose to mention it here, see lesson CCSS.Math.Content.HSN.CN.C.9 for suggestions. It's the fifth lesson down at http://www.newmathteacher.net/algebra-2-lessons-complex-number-system.html. Check student work and review any discrepancies. 5. Exit Slip: Solve each equation. Include complex solutions. 1. x2 + 9 = 0 2. 6x2 + 24 = 0 3. x2 + 64 = 0 Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. All Rights Reserved by NewMathTeacher.Net The Complex Number System Name: ____________________ ______ _______ CCSS.Math.Content.HSN.CN.C.7 Date: ______________________ Period: _____ Solve quadratic equations with real coefficients that have complex solutions. Quadratic Formula For an equation in the form: Discriminant Use the discriminant as a quick way to tell how many and what type of solutions you will have: 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 Use the values of a, b, and c to solve for x: −𝑏 ± √𝑏 2 − 4𝑎𝑐 𝑥= 2𝑎 Example: The discriminant (D) is: D = b2 – 4ac If D > 0, then there are 2 real solutions If D = 0, then there is 1 real solutions If D < 0, then there are 2 complex solutions Use the discriminant to test how many solutions the equation to the left has: 3x2 + 5x - 2 = 0 D = b2 – 4ac = a= b= c= Solve each equation. Include complex solutions. 2. x2 + 18 = 0 2. 6x2 + 24 = 0 3. x2 + 49 = 0 4. x2 + 100 = 0 5. 3x2 + 108 = 0 6. x2 + 12 = 0 Be ready to explain to the class the key points of solving quadratic equations with complex solutions! Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. All Rights Reserved by NewMathTeacher.Net