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
Exploring Complex Roots
In exploring the concept of complex roots, students find the axis of symmetry and roots of parabolas. Then, they discuss what makes a solution complex and how to identify functions with complex roots.
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.
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....
Curated OER
Going Back to Your Roots
Who doesn't need to know the Fundamental Theorem of Algebra? Use the theorem to find the roots of a polynomial on a TI calculator. The class explores polynomials with one solution, no real solutions, and two solutions. This less...
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...
Curated OER
Going Back to Your Roots
Investigate the Fundamental Theorem of Algebra and explore polynomial equations to determine the number of factors, the number of roots, and investigate multiplicity of roots.
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....
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...
Curated OER
Analyze Complex Words
What is a complex word, and why is it so important we know what they are? Download this helpful PowerPoint to introduce root/base words, prefixes, and suffixes to your emerging readers. Clear, relevant examples are given, as well as a...
Curated OER
Greek, Latin and Anglo-Saxon Roots to Better Vocabulary
Practice vocabulary skills with this word analysis lesson. Middle schoolers examine the roots of unfamiliar words and use their knowledge of roots to discern meaning through word analysis.
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.
Curated OER
Root Words Worksheet
Explore the parts of words! Fourth and fifth graders study root words with this activity. They combine words with a given prefix and root word, like combat. There are 13 words to combine!
Haut Gap Middle School
Root Words
Scholars demonstrate their knowledge of root words aqua and aud, and develop vocabulary skills by completing of a chart, handout, and worksheet using creative thinking skills, a dictionary, and a thesaurus.
EngageNY
Factoring Extended to the Complex Realm
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...
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.
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
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...
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...
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.
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
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
It's Greek To Me!
In this language lesson, scholars use Greek root meanings to determine the meaning of words. After being shown how Greek roots are used in many words, such as, photosynthesis, pairs are given two excellent black line masters embedded in...