Curated OER
Operations of Complex Numbers and Intro to DeMoivre's Theorem
Pupils solve problems with complex numbers. In this algebra lesson, students factor complex numbers and simplify equations using DeMoivre's Theorem. They add, subtract, multiply and divide using negative roots.
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...
Curated OER
Complex Analysis: Polar & Exponential Forms
In this polar and exponential form instructional activity, students use Euler's Formula to write complex numbers in exponential form. They write numbers in rectangular form. This two-page instructional activity contains seven...
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...
Curated OER
Iterating the Function and Complex Numbers
Students identify the end behavior of polynomial graphs. In this algebra lesson, students factor and solve quadratic and complex equations. They factor out negative roots and identify the real and imaginary parts of an equation.
Curated OER
Imaginary Numbers
In this Algebra II worksheet, 11th graders solve problems that involve determine the value of expression involving the imaginary unit. The one page worksheet contains three multiple choice questions. Answers provided.
EngageNY
End-of-Module Assessment Task — Precalculus (Module 1)
A transformational assessment determines how far pupils are advancing toward mastering complex and matrix standards. The assessment checks the learners' understanding of linear transformations, complex numbers and the complex plane,...
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....
EngageNY
Wishful Thinking—Does Linearity Hold? (Part 1)
Not all linear functions are linear transformations — show your class the difference. The first lesson in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...
Curated OER
Arithmetic Complex Numbers
Students convert quadratic functions from standard form to vertex form. In this algebra lesson, students solve polynomials using synthetic and long division. They derive and apply the remainder theorem and factor theorem.
EngageNY
Matrix Multiplication Is Not Commutative
Should matrices be allowed to commute when they are being multiplied? Learners analyze this question to determine if the commutative property applies to matrices. They connect their exploration to transformations, vectors, and complex...
Easy Work Sheet
Name the Property
In this property worksheet, students examine given problems containing complex numbers. They identify the property used in the problem. This one-page worksheet contains 10 problems.
EngageNY
Obstacles Resolved—A Surprising Result
The greater the degree, the more solutions to find! Individuals find the real solutions from a graph and use the Fundamental Theorem of Algebra to find the remaining factors.
Curated OER
Test Chapter 8 Algebra II
In this radical equations and expressions test, students answer 4 multiple choice and 21 short answer questions.
Curated OER
Complexity
Students perform mathematical operations on complex numbers. After a lecture/demo, students utilize a worksheet imbedded in this plan to gain practice performing operations on complex numbers.
Curated OER
Chapter 9 - Objective 3.1 Radicals & Imaginary Numbers
In this imaginary numbers learning exercise, learners solve radical equations containing imaginary numbers. They multiply, divide, subtract and add problems. This one-page learning exercise contains ten problems.
Curated OER
Algebra II Worksheet
For this Algebra II worksheet, learners match the number to the number set it belongs to. Students are given a list of options such as natural, real, complex, and a number that corresponds to on set of options. There are 6 questions.
Chapman University
Fundamental Theorems of Mathematics
There are four fundamental theorems of mathematics: arithmetic, algebra, calculus, and linear algebra listed here. Each one is described on this poster or handout. The challenge for a student of math is to figure out why they are true.
Curated OER
Boolean Algebra
For this physics worksheet, students complete circuit true tables and solve 67 questions on Boolean algebra. They identify different logic gate circuits.
EngageNY
Polynomial, Rational, and Radical Relationships
This assessment pair goes way beyond simple graphing, factoring and solving polynomial equations, really forcing learners to investigate the math ideas behind the calculations. Short and to-the-point questions build on one another,...
Mathematics Vision Project
Module 3: Numbers and Operations
Bring some concrete reasoning to the skills of multiplying and combining terms. Using various strategies, the six activities in the module provide practice for the skills of adding, subtracting, multiplying, and diving polynomials. The...
EngageNY
Comparing Methods—Long Division, Again?
Remember long division from fifth grade? Use the same algorithm to divide polynomials. Learners develop a strategy for dividing polynomials using what they remember from dividing whole numbers.
Curated OER
Fundamental Theorem of Algebra
In this worksheet, learners identify the Fundamental Theorem of Algebra. They solve polynomial functions and simplify expressions and equations.
Curated OER
Irrational and Imaginary Root Theorems
In this irrational and imaginary root theorem worksheet, students identify the number of complex zeros for a given function. They write a polynomial function of leas degree with integral coefficients. This four-page worksheet contains 22...