Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.

MAT-12.NO.12 Extend polynomial identities to the complex numbers.

MAT-12.NO.06 Know there is a complex number i such that i² = -1, and every complex number has the form of a + bi with a and b real. Understand the hierarchal relationships among subsets of the complex number system.

MAT-12.NO.07 Use the definition i 2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

MAT-12.NO.08 Use conjugates to find quotients of complex numbers.

MAT-12.NO.09 Apply the Fundamental Theorem of Algebra to determine the number of zeros for polynomial functions. Find all solutions to a polynomial equation.

MAT-12.AR.11 Solve quadratic equations with real coefficients that have solutions of the form a+bi and a-bi.

MAT-12.NO.10 Represent complex numbers on the complex plane in rectangular, trigonometric, and polar forms. Find the modulus (absolute value) of a complex number. Explain why the rectangular, trigonometric, and polar forms of a given complex number represent the same number.

MAT-12.NO.11 Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.

MAT-12.NO.12Extend polynomial identities to the complex numbers.

MAT-12.NO.13 Apply the Fundamental Theorem of Algebra to find all roots of a polynomial equation and determine the nature (i.e., integer, rational, irrational, real, complex) of the roots.

Equivalent Expressions

MAT-06.AR.EE.03 Identify when two expressions are equivalent. Apply the properties of operations to generate equivalent expressions.

MAT-07.AR.EE.01 Apply the properties of operations as strategies to add, subtract, factor, and expand linear expressions involving variables, integers, and/or non-negative fractions and decimals with an emphasis on writing equivalent expressions.

MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.

MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.

MAT-09.AR.01 Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.

MAT-09.AR.02 Rearrange formulas to isolate a quantity or variable(s) of interest using the same reasoning as in solving equations.

MAT-09.AR.07 Rearrange multi-variable formulas to highlight a quantity of interest.

MAT-09.AR.F.06 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.

MAT-12.NO.02 Perform operations on complex radical expressions to write a simplified equivalent expression.

MAT-12.AR.01 Rearrange multi-variable formulas to highlight a quantity of interest.

MAT-12.AR.02 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.

MAT-12.AR.04 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

MAT-12.AR.05 Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system analogous to rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.

MAT-12.AR.F.03 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.

MAT-12.GM.01 Write the equation of a conic section given its special features. Convert between the standard form and general form equations of conic sections.

MAT-12.GM.02 Identify key features of a conic section given its equation. Apply properties of conic sections in context.

MAT-12.NO.12 Extend polynomial identities to the complex numbers.