Curated OER
Powers and Roots of Complex Numbers
Explore a few powers of complex numbers numerically and decide if there is a pattern and use parametric equations to represent a complex number graphically. Use De Moivre's theorem to represent the roots of the complex number...
Alabama Learning Exchange
Imaginary Numbers? What Do You Mean Imaginary?
Don't worry, this resource actually exists. Scholars learn about imaginary numbers and work on problems simplifying square roots of negative numbers. As an extension, they research the history of imaginary numbers.
Curated OER
Who am I? Find A Polynomial From Its Roots
High schoolers generate the equation of a polynomial given its roots and the end behavior of the function. They need to apply theorems concerning the multiplicity of roots, conjugates of irrational or imaginary roots to find a...
Alabama Learning Exchange
Classifying Complex Numbers
Imaginary numbers are a real thing. Scholars learn about complex numbers, real numbers, and imaginary numbers. They classify given numbers as strictly complex, strictly real, or strictly imaginary in an individual or group activity.
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...
EngageNY
An Appearance of Complex Numbers 1
Complex solutions are not always simple to find. In the fourth lesson of the unit, the class extends their understanding of complex numbers in order to solve and check the solutions to a rational equation presented in the first lesson....
Ohio Department of Education
The Solution is Complex
Consider complex numbers, roots, and quadratic equations. Use the discriminate as a way to determine the nature of a quadratic's roots. Then discuss the similarities and differences between quadratics with two, one, or no real roots....
Alabama Learning Exchange
As If Numbers Weren't Complex Enough Already!
The class explores the concept of complex numbers on a website to generate their own Mandelbrot sets. They will practice performing operations with complex numbers and then to get a visual understanding, graph the absolute value of a...
Curated OER
The Complex Numbers
For this algebra worksheet, students solve 16 problems involving imaginary numbers. In the first three, students find the square root of 3 negative numbers in terms of i. Nine problems involve addition, subtraction, multiplication 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....
Curated OER
Complex Roots: A Graphical Solution
Using their Ti-Nspire to determine the solutions of parabolas, young scholars explore the concept of complex roots. Students determine if parabolas have real or complex roots. Young scholars determine the the axis of symmetry and the...
Curated OER
Roots, Multiplicities, and Factoring Polynomials
In this polynomials worksheet, students find zeros, state multiplicities, and factor twenty-two polynomials. Students then find a polynomials that satisfies the stated conditions in eighteen problems, Finally, students factor...
Alabama Learning Exchange
Complex Numbers Solutions
Complex doesn't have to mean harder! Learners experiment with online software to determine the quadratic equations with complex solutions. They use the quadratic formula to solve equations with both real and complex solutions.
Math About
Introduction to Complex Numbers
In this complex number instructional activity, 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 instructional...
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...
Project Maths
Complex Number Operations
What do animated videos have to do with mathematics? Using operations of complex numbers and their representations on the complex plane, high schoolers observe how mathematics could be used to move animations. The lesson provides an...
Curated OER
Imaginary and complex Numbers
In this Algebra II worksheet, 11th graders simplify expression involving imaginary and complex numbers and determine the quadratic equation that would have the given complex roots. The on page worksheet contains thirty-four problems. ...
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...
EngageNY
Does Every Complex Number Have a Square Root?
Help the class find a better way. Pupils recall finding nth roots or a complex number in polar form from a previous module to find the square root of a complex number. Using the second installment in a series of 23, scholars discover it...
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.
Curated OER
Algebra II Test covering Radicals, Complex Numbers, and Finding Roots of Quadratics
In this algebra two worksheet, students solve twenty-five problems in test format. The worksheet covers radicals, complex numbers, and finding roots of quadratics.
Curated OER
Solving Quadratic Equations with Complex Roots
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...
Curated OER
Complex Numbers
In this complex numbers worksheet, 9th graders solve 10 different problems that include addition and subtraction of these numbers. First, they add or subtract the coefficients of similar terms algebraically. Then, students remove the...
EngageNY
Solving Quadratic Equations by Completing the Square
Many learners find completing the square the preferred approach to solving quadratic equations. Class members combine their skills of using square roots to solve quadratics and completing the square. The resource incorporates a variety...