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...

Challenge the class to prove that the dilation properties always hold. The lesson develops an informal proof of the properties of dilations through a discussion. Two of the proofs are verified with each class member performing the...

The coordinate plane is a popular place! Identify rotations, reflections, and dilations on the coordinate plane. Pupils work in small groups to match transformations of a figure with the description of the transformation. They perform...

Use the coordinate plane to show two figures are similar. The lesson incorporates congruence transformations and dilations to move a figure on to another figure. Pupils determine that if a similarity transformation exists...

Your learners combine their knowledge of real and imaginary numbers and matrices in an activity containing thirty lessons, two assessments (mid-module and end module), and their corresponding rubrics. Centered on complex numbers and...

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...

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...

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...

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...

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...

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 lesson 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 lesson breaks the process of reflecting across a line...

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

Pupils work in pairs to investigate what it takes to prove that two triangles are similar. They work through various shortcuts to find which are enough to show a similarity relationship between the triangles. Small groups work with the...