The Complex Number System Name: ____TEACHER COPY ______ _______ CCSS.Math.Content.HSN.CN.C.8 Date: ______________________ Period: _____ Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x - 2i). 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, polynomial, 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) Solve each equation. Include complex solutions. A. x2 + 18 = 0 B. 6x2 + 24 = 0 C. x2 + 49 = 0 Check student work and review any discrepancies. 4. Independent Practice : Students will review the properties involved in factoring polynomials and apply them in problems that involve complex number solutions. After reviewing the guided practice as a group or with partners, have the students work independently on the specific examples on the worksheet below. 5. Exit Slip: 1. List three complex numbers. 2. What is another way of expressing √−9 ? 3. What is the value of the square of i ? 4. What is the real part of the complex number 2 + 3i ? 5. What is the imaginary part of the complex number 2 + 3i ? 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.8 Date: ______________________ Period: _____ Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x - 2i). Review of Polynomials with Real Solutions Classify the polynomial by the number of terms and state the degree of the polynomial. Polynomial Monomial, Trinomial, Binomial Degree 1. 3x3y4 2. x5 – 2x3 - 4 3. 2y + 5 Write the polynomial so that the exponents are in descending order. 4. (3x + 5) + (2x - 3) 3x 2x +5 -3 5. (3x + 5)(2x - 3) Factor out the greatest common monomial factor. 6. 7x2 - 7x = ____ ( 7. x2 - 4x - 5 = ( ) )( ) For an equation in the form: Solve the equation for x. 8. ( 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 x2 - 4x - 5 = 0 )( )=0 9. x2 = 8x x2 - ___ = 0 Use the values of a, b, and c to solve for x: 𝑥= −𝑏 ± √𝑏 2 − 4𝑎𝑐 2𝑎 Polynomials with Complex Solutions Solve each equation. Include complex solutions. Use factoring for #10-15 and the quadratic equation for #16-18. 10. x2 + 16 = 0 11. 2x2 + 18 = 0 12. x2 + 36 = 0 13. x2 + 81 = 0 14. 3x2 + 12 = 0 15. x2 + 8 = 0 16. -x2 + 3x - 3 = 0 17. 6x2 + 5x + 4 = 0 18. 4x2 - 3x + 2 = 0 Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. All Rights Reserved by NewMathTeacher.Net