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Lesson Plan
Curated OER

Radicals: Addition & Subtraction of Complex Numbers

For Teachers 10th - 12th Standards
In this radical worksheet, students simplify complex numbers.  They find the sum and difference of complex numbers.  This two-page worksheet contains 11 multiple-choice problems.  Answers are given on the last page.
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Worksheet
Math About

Introduction to Complex Numbers

For Students 10th - 12th Standards
In this complex number worksheet, students explore the properties of imaginary numbers to find the square roots of negative numbers. Explanations and examples are given prior to the exercise. This two-page worksheet contains ten problems.
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Lesson Plan
Illustrative Mathematics

Irrational Numbers on the Number Line

For Teachers 7th - 9th Standards
There are four irrational numbers that participants need to graph. Pi(π), -(½ x π), and √17 are easy to approximate with common rational numbers. On the other hand, the commentary describing the irrational number 2√2 is not clear. It...
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Lesson Plan
EngageNY

Factoring Extended to the Complex Realm

For Students 10th - 12th Standards
A solution will work one way or another: find solutions, or use solutions to find the function. Learners use polynomial identities to factor polynomials with complex solutions. They then use solutions and the Zero Product Property to...
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Lesson Plan
EngageNY

Curves in the Complex Plane

For Teachers 11th - 12th Standards
Go around and around on the complex plane. The sixth lesson in a 23-part unit reviews representing numbers in the complex plane. Pupils graph numbers with equal moduli and notice they represent a circle. They continue to explore complex...
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Unit Plan
2
2
Mathematics Vision Project

Quadratic Equations

For Teachers 10th - 12th Standards
Through a variety of physical and theoretical situations, learners are led through the development of some of the deepest concepts in high school mathematics. Complex numbers, the fundamental theorem of algebra and rational exponents...
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Lesson Plan
Curated OER

Imaginary Numbers

For Teachers 11th
In this Algebra II worksheet, 11th graders explain how every real number is also a complex number.  The one page worksheet contains one problem with solution. 
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Interactive
Curated OER

Complex Number Multiplication

For Students 10th - 12th
In this multiplication activity, students multiply complex numbers.  This interactive one-page activity contains 10 problems.  Answers are provided.
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Lesson Plan
Curated OER

Complex Numbers

For Teachers 10th - 12th
In this complex numbers worksheet, students write numbers as a multiple of i. They add and subtract imaginary numbers. Students write complex quotients in standard form. This three-page worksheet contains six problems.
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Worksheet
Kuta Software

Simplifying Radicals/Imaginary Numbers

For Students 9th - 12th Standards
Looking for straightforward practice on simplifying radicals and imaginary numbers? Here are 20 problems to practice these skills and an answer key for the odd-numbered questions. 
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Lesson Plan
EngageNY

Solutions to Polynomial Equations

For Teachers 11th - 12th Standards
Take a step back to Algebra II. The first lesson plan in a series of 23 asks scholars to remember working with quadratic equations with complex solutions. Pupils apply polynomial identities to complex numbers and work examples that show...
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Worksheet
Curated OER

Complex Number

For Students 8th - 10th
In this algebra worksheet, students identify the vertex of a quadratic functions. They identify complex numbers. There are 6 questions.
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Worksheet
Curated OER

Complex Analysis: Graphical Representations

For Students Higher Ed
In this graphical representation worksheet, students draw an Argand diagram depicting two complex numbers in a complex plane. They draw vectors to represent complex numbers. This two-page worksheet contains five equations to solve.
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Worksheet
Curated OER

Complex Analysis: Graphical Representations

For Students Higher Ed
In this graphical representation activity, students draw an Argand diagram depicting complex numbers. They draw in vectors that represent complex numbers. This three-page activity contains approximately ten problems.
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Lesson Plan
Curated OER

Operations of Complex Numbers and Intro to DeMoivre's Theorem

For Teachers 9th - 10th
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.
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Worksheet
Curated OER

Complex Analysis: Complex Numbers

For Students Higher Ed
In this complex numbers worksheet, students compute the value of given expressions and write the answer in complex number form. This one-page worksheet contains three equations.
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Worksheet
Curated OER

Complex Analysis: Polar Form

For Students Higher Ed
In this polar form worksheet, students write complex numbers in polar form. They draw an Argand diagram containing vectors and draw sketches representing in a coordinate plane. This two-page worksheet contains thirteen multi-step...
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Worksheet
Curated OER

Solving Quadratic Equations with Complex Roots

For Students 8th - 9th
In this quadratic equations instructional activity, students solve 10 different equations that include complex roots. First, they solve for the indicated variable and express the roots of the equation in simplest form. Then, students...
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Lesson Plan
EngageNY

Exploiting the Connection to Trigonometry 2

For Teachers 11th - 12th Standards
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...
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Lesson Plan
EngageNY

The Geometric Effect of Multiplying by a Reciprocal

For Teachers 11th - 12th Standards
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...
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Lesson Plan
EngageNY

Exploiting the Connection to Cartesian Coordinates

For Teachers 11th - 12th Standards
Multiplication in polar form is nice and neat—that is not the case for coordinate representation. Multiplication by a complex number results in a dilation and a rotation in the plane. The formulas to show the dilation and rotation are...
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Worksheet
Curated OER

Complex Analysis: Polar & Exponential Forms

For Students Higher Ed
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...
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Lesson Plan
EngageNY

Exploiting the Connection to Trigonometry 1

For Teachers 11th - 12th Standards
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...
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Assessment
EngageNY

Mid-Module Assessment Task - Precalculus (module 1)

For Teachers 11th - 12th Standards
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...

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