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...

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

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...

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

Complex solutions are not always simple to find. In the fourth lesson 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 first lesson....

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...

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...

Translating complex numbers is as simple as adding 1, 2, 3. In the ninth activity 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...

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...

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...

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...

A transformational assessment determines how far pupils are advancing toward mastering complex and matrix standards. The assessment checks the learners' understanding of linear transformations, complex numbers and the complex plane,...

Individuals show what they know about the geometric representations of complex numbers and linearity. Seventeen questions challenge them to demonstrate their knowledge of moduli and operations with complex numbers. The assessment is...

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...

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...

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...

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...

Using their Ti-Nspire to determine the solutions of parabolas, students explore the concept of complex roots.  Students determine if parabolas have real or complex roots.  Students determine the the axis of symmetry and the...

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...

In this precalc lesson, students write out definitions, identify functions, solve integrals and derivatives and graph trig functions as they relate to angles. This is a final exam for precalculus. There are 80 questions on this exam.

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

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.

In this precalculus worksheet, students write numbers in their trigonometric form and compute the numbers to a given power. Students explore the parametric function and trace the roots of unity. After completing eight short answer...