Curated OER
Complex Number
In this algebra worksheet, students identify the vertex of a quadratic functions. They identify complex numbers. There are 6 questions.
Curated OER
Complex Analysis: Graphical Representations
In this graphical representation activity, students draw an Argand diagram depicting complex numbers. They draw in vectors that represent complex numbers. This three-page activity contains approximately ten problems.
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Operations of Complex Numbers and Intro to DeMoivre's Theorem
Pupils solve problems with complex numbers. In this algebra lesson, students factor complex numbers and simplify equations using DeMoivre's Theorem. They add, subtract, multiply and divide using negative roots.
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Complex Analysis: Polar Form
In this polar form worksheet, students write complex numbers in polar form. They draw an Argand diagram containing vectors and draw sketches representing in a coordinate plane. This two-page worksheet contains thirteen multi-step...
EngageNY
Exploiting the Connection to Trigonometry 2
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 how to reverse...
EngageNY
The Geometric Effect of Multiplying by a Reciprocal
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...
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Exploiting the Connection to Cartesian Coordinates
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...
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Complex Analysis: Polar & Exponential Forms
In this polar and exponential form instructional activity, students use Euler's Formula to write complex numbers in exponential form. They write numbers in rectangular form. This two-page instructional activity contains seven...
EngageNY
Exploiting the Connection to Trigonometry 1
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 number. Groups...
EngageNY
Mid-Module Assessment Task - Precalculus (module 1)
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...
Curated OER
Real and Complex Conjugates
Students explore examples of real binomial conjugates involving the square root of negative one. In a class setting, students study examples of complex conjugates and work given problems. They play "Find My Conjugate" game where real and...
EngageNY
End-of-Module Assessment Task — Precalculus (Module 1)
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,...
EngageNY
Roots of Unity
Visualize the nth roots of unity. Pupils calculate the nth roots of unity and find all n roots. Learners plot the solutions in the complex plane and observe that they are the vertices of a regular n-gon inscribed in the unit circle....
Curated OER
Iterating the Function and Complex Numbers
Students identify the end behavior of polynomial graphs. In this algebra lesson, students factor and solve quadratic and complex equations. They factor out negative roots and identify the real and imaginary parts of an equation.
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Complex Number Subtraction
In this subtraction learning exercise, students find the difference of complex numbers. This one-page learning exercise contains 10 problems. Answers are provided.
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Complex Number Division
In this online math worksheet, learners practice complex number division using positive and negative integers. When complete, students submit their answers and get instant feedback regarding their accuracy.
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Quaternions
For this quaternions worksheet, students solve and complete 7 different problems. First, they read and identify quaternions as expressions in a given form of ordinary real numbers. Then, students add and subtract a few problems by doing...
EngageNY
Matrix Multiplication Is Not Commutative
Should matrices be allowed to commute when they are being multiplied? Learners analyze this question to determine if the commutative property applies to matrices. They connect their exploration to transformations, vectors, and complex...
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Complex Analysis: Polynomial Equations
For this polynomial equation worksheet, students explore real fractional powers of complex numbers. This three-page worksheet contains examples, explanations and approximately seven problems.
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Steady-State Circuit Analysis & Filter Design
Scholars identify how the TI-89 implements phasors to perform sinusoidal steady-state analysis. The focus is on how to enter and display complex numbers. They also show how a typical steady-state application how to use the Numeric Solver...
Curated OER
Complex Roots: A Graphical Solution
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 vertex given...
Easy Work Sheet
Name the Property
In this property activity, students examine given problems containing complex numbers. They identify the property used in the problem. This one-page activity contains 10 problems.
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Complexity
Students perform mathematical operations on complex numbers. After a lecture/demo, students utilize a worksheet imbedded in this plan to gain practice performing operations on complex numbers.
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Arithmetic Complex Numbers
Students convert quadratic functions from standard form to vertex form. In this algebra lesson, students solve polynomials using synthetic and long division. They derive and apply the remainder theorem and factor theorem.
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