#### MAT-12.NO.08

 12th Grade (MAT) Targeted Standard    (NO) Number and Operations  Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.

## Progressions

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.12 Extend 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.