Mathematics Curriculum Framework
November 2000

## Learning Standards

### Number Sense and Operations for Grades 11-12 Understand numbers, ways of representing numbers, relationships among numbers, and number systems Understand meanings of operations and how they relate to one another Compute fluently and make reasonable estimates

#### Learning Standards

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
 12.N.1 Define complex numbers (e.g., a + bi) and operations on them, in particular, addition, subtraction, multiplication, and division. Relate the system of complex numbers to the systems of real and rational numbers. 12.N.2 Simplify numerical expressions with powers and roots, including fractional and negative exponents.

#### Exploratory Concepts and Skills for Grades 11-12 and Single-Subject Courses

• Investigate special topics in number theory, e.g., the use of prime numbers in cryptography.
• Use polar-coordinate representations of complex numbers (i.e., a + bi = r(cos? + isin?)) and DeMoivre's theorem to multiply, take roots, and raise numbers to a power.
• Plot complex numbers using both rectangular and polar coordinate systems.

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