Standard 4 : Polar Coordinates and Trigonometric Form of Complex Numbers (Archived)



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Define, use polar coordinates, and relate them to Cartesian coordinates. Translate equations in terms of Cartesian coordinates into polar coordinates, and graph the resulting equations in the polar coordinate plane. Convert complex numbers from standard to trigonometric form, and vice-versa. Multiply complex numbers in trigonometric form, and use De Moivre’s Theorem.

General Information

Number: MA.912.T.4
Title: Polar Coordinates and Trigonometric Form of Complex Numbers
Type: Standard
Subject: X-Mathematics (former standards - 2008) - Archived
Grade: 912
Body of Knowledge: Trigonometry

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.T.4.1: Define polar coordinates and relate polar coordinates to Cartesian coordinates with and without the use of technology.
MA.912.T.4.2: Represent equations given in rectangular coordinates in terms of polar coordinates.
MA.912.T.4.3: Graph equations in the polar coordinate plane with and without the use of graphing technology.
MA.912.T.4.4: Define the trigonometric form of complex numbers, convert complex numbers to trigonometric form, and multiply complex numbers in trigonometric form.
MA.912.T.4.5: Apply DeMoivre's Theorem to perform operations with complex numbers.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Image/Photograph

Name Description
Clipart ETC: Trigonometry and Analytic Geometry: Clipart for Trigonometry and Analytic Geometry

Video/Audio/Animation

Name Description
MIT BLOSSOMS - Fabulous Fractals and Difference Equations :

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations.



Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Video/Audio/Animation

Title Description
MIT BLOSSOMS - Fabulous Fractals and Difference Equations :

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations.