When working with matrix multiplication, it all comes back around. The 31st portion of the unit is the third lesson on inverse matrices. The resource reviews the concepts of inverses and how to find them from the previous two lessons....

Help the class visualize operations with complex numbers with a lesson that formally introduces complex numbers and reviews the visualization of complex numbers on the complex plane. The fifth installment of a 32-part series reviews...

Calculate exact trigonometric values using the angles of special right triangles. Beginning with a review of the unit circle and trigonometric functions, class members use their knowledge of special right triangles to find the value...

Use the graphs of the trigonometric functions to set the stage to inverse functions. The lesson reviews the graphs of the basic trigonometric functions and their transformations. Pupils use their knowledge of graphing functions to model...

Construct tangent lines and make the connection to tangent functions. An informative lesson reviews the geometry origins of the tangent function. Pupils use that information to determine how to construct a tangent to a circle from a...

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...

Revisit the relationship between logarithms and exponentials. Learners review the notion of logarithms as the way to solve exponential equations in the 21st segment in a Pre-calculus series of 23. Pupils use the knowledge to prove that...

Investigate patterns in the binomial theorem. Pupils begin by reviewing the coefficients from Pascal's triangle. They look at the individual terms, the sums of the coefficients on a row, and the alternating sum of each row. Individuals...

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...

Make a connection between rational expressions and rational functions. Pupils review simplifying and performing operations on rational expressions and recall what it means for two rational expressions to be equivalent based on their...

Find out when rational expressions are closed. Pupils review adding, subtracting, multiplying, and dividing with rational numbers to make the connections to operations with rational expressions. Using specific examples, learners notice...

Complex numbers were first represented on the complex plane, now they are being represented using sine and cosine. Introduce the class to the polar form of a complex number with the 13th part of a 32-part series that defines the...

Translating complex numbers is as simple as adding 1, 2, 3. In the ninth lesson in a 32-part series, the class takes a deeper look at the geometric effect of adding and subtracting complex numbers. The resource leads pupils into what it...

In the 16th instructional activity in the series of 32 the class uses the concept of complex multiplication to build a transformation in order to reflect across a given line in the complex plane. The instructional activity breaks the...

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...

The second day of a two-part lesson plan on motion introduces the class to circular motion. Pupils learn how to incorporate a time parameter into the rotational matrix transformations they already know. The 24th installment in the...

Show your math class how to use vectors in adding complex numbers. Vectors represent complex numbers as opposed to points in the coordinate plane. The class uses the geometric representation to add and subtract complex numbers and...

The 10th lesson in a series of 32, continues with the geometry of arithmetic of complex numbers focusing on multiplication. Class members find the effects of multiplying a complex number by a real number, an imaginary number, and another...

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...

Use 2x2 matrices to move along a line. The second day of a two-day lesson is the 28th installment in a 32-part unit. Pupils work together to create and solve systems of equations that will map a transformation to a given...

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...

Use a triangle area formula that works when the height is unknown. The eighth installment in a 16-part series on trigonometry revisits the trigonometric triangle area formula that previously was shown to work with the acute triangles....

Build on the understanding of finding angles using trigonometric ratios. Pupils develop the definitions of inverse trigonometric functions by restricting their domains in the 13th lesson of a 16-part series. They use inverse functional...

Take a step back to Algebra II. The first lesson 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 how...