EngageNY
Complex Numbers and Transformations
Your learners combine their knowledge of real and imaginary numbers and matrices in an activity containing thirty lessons, two assessments (mid-module and end module), and their corresponding rubrics. Centered on complex numbers and...
EngageNY
Roots of Unity
Visualize the nth roots of unity. Pupils calculate the nth roots of unity and find all n roots. Learners plot the solutions in the complex plane and observe that they are the vertices of a regular n-gon inscribed in the unit circle....
CK-12 Foundation
Find Imaginary Solutions: Imaginary Zeros
The resource is the real deal. Individuals investigate the imaginary zeros of f(x) = x^2 + 1. They accomplish this task by using an interactive that shows input values x = a + bi and output values x^2 + 1 on a complex plane.
Curated OER
Complex Analysis: Point Sets in the Complex Plane
In this point set instructional activity, students explore definitions describing planar point sets. They use the definitions to describe examples of point sets. This two-page instructional activity contains four problems and 15...
Thomson Brooks-Core
Complex Numbers
A straightforward approach to teaching complex numbers, this lesson addresses the concepts of complex numbers, polar coordinates, Euler's formula, De moivres Theorem, and more. It includes a practice problems set with odd answers and a...
Curated OER
Space Shuttle's Heat Shield Problem
High schoolers participate in a role-play activity to determine how to replace heat shields on the space shuttle using polar coordinates.
EngageNY
The Geometric Effect of Multiplying by a Reciprocal
Class members perform complex operations on a plane in the 17th segment in the 32-part series. Learners first verify that multiplication by the reciprocal does the same geometrically as it does algebraically. The class then circles back...
EngageNY
Exploiting the Connection to Trigonometry 2
The class checks to see if the formula for finding powers of a complex number works to find the roots too. Pupils review the previous day's work and graph on the polar grid. The discussion leads the class to think about how to reverse...
Curated OER
Complex Roots Made Visible
In this algebra worksheet, 11th graders solve quadratic functions using the quadratic formula. They identify the negative roots using complex roots. There is an answer key with this problem.
Curated OER
Complex numbers in polar form
Young scholars plot complex numbers in the polar plane. They convert complex numbers in polar form to rectangular form. Students plot coordinates in the polar plane. They plot complex numbers in the complex plane. Young scholars are...
Curated OER
Complex Analysis: Graphical Representations
In this graphical representation instructional activity, students draw an Argand diagram depicting two complex numbers in a complex plane. They draw vectors to represent complex numbers. This two-page instructional activity contains...
CK-12 Foundation
DeMoivre's Theorem and nth Roots: The nth Roots of Unity
The nth roots of unity all have a magnitude of one. Scholars use the unit circle and DeMoivre's Theorem to find the complex roots of one and discover that the complex numbers all lie on the unit circle and are equally spaced around it...
Curated OER
Complex Numbers
In this algebra worksheet, 11th graders solve complex numbers using division. multiplication, addition and subtraction. There are 11 questions with an answer key.
Colorado Unit Writing Project
Simple Machines
Planning an elementary science unit has never been simpler! These twelve lessons guide young scientists through an exploration of simple machines and their many uses in the real world before asking them to apply their learning in the...
Curated OER
Complex Analysis: Function
In this function worksheet, students evaluate problems involving functions, identify the domain and range of functions, and complete inversion mapping. This two-page worksheet contains approximately twelve problems.
EngageNY
Mid-Module Assessment Task - Precalculus (module 1)
Individuals show what they know about the geometric representations of complex numbers and linearity. Seventeen questions challenge them to demonstrate their knowledge of moduli and operations with complex numbers. The assessment is the...
Kuta Software
Imaginary Numbers
Here is a worksheet that takes all aspects of quadratic functions and incorporates imaginary numbers into the problems. The problems range from simplifying to graphing and solving by using a variety of methods with imaginary and complex...
Curated OER
Ellipses and Kepler's First Law
The class examines graphs in the form r = F(¿¿) in polar coordinates (r, ¿¿), in particular with the circle, ellipse and other conic sections. They determine the nature of an ellipse by studying the role of the semimajor axis and...
EngageNY
A Surprising Boost from Geometry
Working with imaginary numbers — this is where it gets complex! After exploring the graph of complex numbers, learners simplify them using addition, subtraction, and multiplication.
EngageNY
Exploiting the Connection to Trigonometry 1
Class members use the powers of multiplication in the 19th installment of the 32-part unit has individuals to utilize what they know about the multiplication of complex numbers to calculate the integral powers of a complex number. Groups...
Curated OER
Points in a Complex Plane -- Lecture
Students review plotting points on a coordinate plane. Individually, they add and subtrace complex numbers and graph them in a complex plane. They follow along a worksheet while their teacher lectures on the new material and solve...
Curated OER
Points in the Complex Plane -- Lab
Middle schoolers review the lecture portion of this lesson. Individually, they graph various points on a complex plane and identify conjugates based on their location on the graphs. They complete a worksheet and review their answers to...
Curated OER
Simple/Complex Machines
Learners make a simple machine. In this physics instructional activity, students learn about six types of simple machines and the purpose of each and brainstorm examples of simple and complex machines in the classroom. Learners create a...
Curated OER
Complex numbers in polar form
Students plot complex numbers in the polar plane. They are asked to list what they believe are the five most famous numbers in mathematics. Students are explained that generally accepted that the five most famous numbers in mathematics...