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A2-N-1-1

Page history last edited by Tashe Harris 6 years, 2 months ago

A2.N.1.1 Find the value of iⁿ for any whole number n.

In a Nutshell

By defining imaginary numbers, students can now apply the square root function to any real number and obtain a real or imaginary solution.They can solve in for any real number n.

Student Actions	Teacher Actions
Students will develop a deep and flexible understanding of the definition of imaginary numbers ().Students will develop procedural fluency as they look for and make use of patterns in for any real number n. Students will develop the ability to make conjectures and generalize iⁿ. Students will develop mathematical reasoning as they define and graph complex numbers.	Facilitate meaningful mathematical discourse by providing students with opportunities to discover the need for imaginary numbers. Build procedural fluency from conceptual understanding by providing tasks for students to use the properties of powers to help simplify powers of i. Support productive struggle in learning mathematics by allowing students to explore the concept of multiplying by i to be 90 degree rotation about the origin in the complex plane. Students should describe what happens at i, i², i³, i⁴, and how the pattern repeats after 360 degrees.
Key Understandings	Misconceptions
Expand knowledge of numbers to include imaginary numbers. Understand that in repeats every 4 iterations. Introduction to the complex plane.	Conceptual: Students believe the set of all numbers include only real numbers and imaginary numbers are an artificial addition. Students identify i as a variable rather than a number.