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Reasoning with Equations and Inequalities- A-REI ELG.MA.HS.A.9: Solve equations and inequalities in one variable. A-REI.4 Solve quadratic equations in one variable. A-REI.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form. A-REI.4.b Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. The Complex Number System – N-CN ELG.MA.HS.N.6: Use complex numbers in polynomial identities and equations. N-CN.C.8 (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i). N-CN.C.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Algebra 2: The Complex Number System – N-CN ELG.MA.HS.N.6: Use complex numbers in polynomial identities and equations. N-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions. Students will demonstrate command of the ELG by: Extending polynomial identities to the complex numbers. Showing that the Fundamental Theorem of Algebra is true for quadratic polynomials. Vocabulary: Complex solution Fundamental Theorem of Algebra Polynomial identity Quadratic polynomial Sample Assessment Questions: 1) Standard(s): N-CN.A.2 N-CN.B.5 N-CN.C.8 Source: https://www.illustrativemathematics.org/content-standards/HSN/CN/C/8/tasks/1659 Item Prompt: For each odd positive integer n, the only real number solution to xn=1 is x=1 while for even positive integers n, x=1 and x=−1 are solutions to xn=1. In this problem we look for all complex number solutions to xn=1 for some small values of n. a. Find all complex numbers a+bi whose cube is 1. b. Find all complex numbers a+bi whose fourth power is 1. Correct Answer: Solution: 2 Using Geometry (go to source link above) Solution: 3 Solving Equations (go to source link above)