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
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
Algebra I: nth Root and Rational Exponents
This algebra worksheet contains problems on converting between nth roots and rational exponents for numbers. It also includes problems on simplifying radicals having various indices and rational exponents. It does not include an answer...
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...
Curated OER
nth Roots and Rational Exponents
In this algebra worksheet, students evaluate 20 problems in which they work with nth roots and rational exponents. They write expressions using rational exponents and radical notation. They identify roots, and round answers to two...
Curated OER
Rational Exponents
Investigate rational exponents in this math lesson. Scholars make conjectures about the relationship between rational exponents and radicals. They then use their Ti-Nspire to simplify rational exponents.
Curated OER
Complex Analysis: Polynomial Equations
In this polynomial equations worksheet, students evaluate roots and draw vector representations. This three-page worksheet contains four problems.
Curated OER
Roots and Radical Expressions
In this Algebra II worksheet, 11th graders simplify radical expressions. The two page worksheet contains explanation, worked example, and three practice problems. Answers are not included.
Curated OER
Complex Analysis: Polynomial Equations
For this polynomial equation worksheet, students explore real fractional powers of complex numbers. This three-page worksheet contains examples, explanations and approximately seven problems.
Curated OER
Exploring Function Graphs
Tenth graders investigate three different sets of data that relate temperature to another variable in the physical world. These illustrate linear, inverse and exponential relationships.