Complex Numbers Teacher Resources

In this rationalizing denominators worksheet, students rationalize imaginary denominators in twenty-six problems.  Sixteen of the problems have denominators that are monomials and ten binomials.  The solutions are provided.

In this mathematics instructional activity, students solve problems about numerous high school topics including trigonometry, algebra, and pre-calculus. This instructional activity contains, but is not limited to, radicals, inverse...

In this sigma worksheet, students evaluate patterns. They find the sum of the digits in a sequence and write the formula to produce the sequence. This one page worksheet contains four multi-step problems.

In this video on the Binomial Theorem, Sal tries to give an intuition behind why combinations are part of its definition. By looking at the expansion of (a + b)3 and carefully looking at where each value originates from, one can see how...

Continuing with the lesson on compound interest, in this video, Sal derives the general formula for any amount of principle, interest rate, and compounding periods over one year.

Sal continues to look at changing the length of compounding time, from daily to hourly compounding interest. Now he is able to show that compounding 100% annual interest converges on the number 2.71É or e as the number of compounding...

Here is an example in this video of graphing a hyperbola centered at the origin. First, Sal shows solving for the equations of the asymptotes and then shows how to determine the direction of the hyperbola. He takes the approach of not...

Continuing with the study of graphing hyperbolas, Sal shows an example of graphing a parabola that is centered at a point off the origin. By looking at the equation, first without shifting it, he helps listeners develop an intuitive...

Review the multiple methods of solving quadratic equations through an analysis of the discriminant. Scholars use the discriminant to determine the best solution method and then solve various equations. As a challenge, learners build...

Take a radical look at square roots. The presentation examines square roots as the lengths of the sides of a square with a given area on the coordinate plane. Using this method, it is clear why the square root of a number can be positive...

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.

Time for pupils to use their imagination! Learners examine the relationship between a system with no real solution and its graph. They then verify their discoveries with algebra. 

Trying to find a linear transformation is like finding a needle in a haystack. The second lesson in the series of 32 continues to explore the concept of linearity started in the first lesson. The class explores trigonometric, rational,...

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...

Students use optimization concepts to design their own container. For this optimization lesson plan, students understand how the optimization concept is critical in calculus and why products are packaged the way they are.

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...

Use everything you know about quadratic equations to solve polynomial equations! Learners apply the Zero Product Property to factor and solve polynomial equations. They make a direct connection to methods they have used with quadratic...

Combine vectors and matrices to describe transformations in space. Class members create visual representations of the addition of ordered pairs to discover the resulting parallelogram. They also examine the graphical representation...

These four problems will guide your class through the idea behind the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n roots. Use the division algorithm and the definition of a zero/root of a...

Start off with the definition of the imaginary number i, then have your class practice simplifying expressions involving powers of i and look for patterns. See how the cyclic nature of powers of i translate to sums of powers of i.

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...

Fourth and fifth graders study the Pythagorean Theorem and apply it to find the missing side of a right triangle.

Have fun while your class creates a timeline of their lives. They record events before and after they were born on a line with 10 integer pairs consisting of one integer on each side of zero. Many extension activities can be done in...

Students investigate the properties behind the quadratic equation. In this algebra instructional activity, students identify quadratic equation in the real world. They graph the parabola and identify the vertex and intercepts.