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**Standard(s): **
[MA2015] AL2 (9-12) 2 :

[MA2015] AL2 (9-12) 4 :

[MA2019] AL1-19 (9-12) 3 :

2 ) Use the relation *i*^{2} = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. [N-CN2]

[MA2015] AL2 (9-12) 4 :

4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]

[MA2019] AL1-19 (9-12) 3 :

3. Define the imaginary number* i* such that *i*^{2} = -1.

[MA2019] AL1-19 (9-12) 9 : 9. Select an appropriate method to solve a quadratic equation in one variable.

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. Explain how the quadratic formula is derived from this form.

b. Solve quadratic equations by inspection (such as *x*^{2} = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real.

In Module 1, Topic D students extend their facility with solving polynomial equations to working with complex zeros. Complex numbers are introduced via their relationship with geometric transformations. The topic concludes with students realizing that every polynomial function can be written as a product of linear factors, which is not possible without complex numbers.