To work through the complexity of coordinate geometry pupils make the connection between the coordinate plane and the complex plane as they plot complex numbers in the 11th part of a series of 32. Making the connection between the two...

To commute or not to commute, that is the question. The 26th segment in a 32-segment lesson focuses on the effect of performing one transformation after another one. The pupils develop the procedure in order to multiply two 2 X 2...

Classmates apply midpoint concepts by leapfrogging around the complex plane. The 12th instructional activity in a 32 segment unit, asks pupils to apply distances and midpoints in relationship to two complex numbers. The class develops a...

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...

Individuals learn to divide and conquer complex numbers with a little help from moduli and conjugates. In the second lesson on complex number division, the class takes a closer look at the numerator and denominator of the multiplicative...

The second day of a two-part lesson 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 32-part...

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...

Conjugating in the math classroom — and we're not talking verbs! The seventh instructional activity in a series of 32 introduces the class to the building blocks of complex number division. During the instruction, the class learns to...

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....

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,...

Help the class visualize operations with complex numbers with a instructional activity that formally introduces complex numbers and reviews the visualization of complex numbers on the complex plane. The fifth installment of a...

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 14th lesson in the unit has the class prove the nine general cases of the geometric representation of complex number multiplication. Class members determine the modulus of the product and hypothesize the relationship for the...

Class members make a real connection to matrices in the 25th part of a series of 32 by looking at the identity matrix and making the connection to the multiplicative identity in the real numbers. Pupils explore different...

Wait, let's start over — teach your class how to return to the beginning. The first lesson looking at inverse matrices introduces the concept of being able to undo a matrix transformation. Learners work with matrices with a determinant...

The second lesson on finding inverse matrices asks class members to look for a pattern in the inverse matrix and test it to see if it works for all matrices. The teacher leads a discussion to refine the process in finding inverses,...

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...

The matrix — it's not just a movie. The lesson introduces the concept of 2 x 2 matrix multiplication as a way to represent linear transformations. Class members determine when a linear transformation represented as matrix...

Does complex number multiplication have the class spinning? Here's a resource that helps pupils explore and discover the geometric effect of multiplying complex numbers. In the 14th installment in the 32-part unit groups look at the unit...

Complex solutions are not always simple to find. In the fourth instructional activity 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...

Not all linear functions are linear transformations — show your class the difference. The first lesson in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...

Not all linear functions are linear transformations, only those that go through the origin. The third lesson in the 32-part unit proves that linear transformations are of the form f(x) = ax. The lesson plan takes another look at examples...

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...