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\n\"Complex\n\n
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\nComplex Numbers: Plotting and Polar Form\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nExplore the concept of, and use the Ti-Nspire to, convert complex numbers into polar form. Then practice graphing complex numbers in the polar coordinate plane.\n
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\n\"Distance\n\n
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\nEngageNY\n
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\nDistance and Complex Numbers 1\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nTo 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...\n
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\n\"Complex\n\n
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\nEngageNY\n
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\nComplex Numbers as Vectors\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nShow 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...\n
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\n\"An\n\n
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\nEngageNY\n
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\nAn Appearance of Complex Numbers 2\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nHelp 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...\n
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Interactive
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\n\"Trigonometric\n\n
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\nCK-12 Foundation\n
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\nTrigonometric Form of Complex Numbers\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nRepresent complex numbers in two ways. Pupils use the interactive to convert polar and rectangular representations of complex numbers. The learners drag an overlay back and forth over the coordinate plane to reveal the polar coordinates...\n
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\n\"Distance\n\n
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\nEngageNY\n
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\nDistance and Complex Numbers 2\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nClassmates 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...\n
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Instructional Video4:07
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\n\"How\n\n
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\nHow Do You Add Complex Numbers by Graphing in the Complex Plane?\n

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\n\nFor Teachers\n\n10th - 11th\n
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\nGraphs usually add an extra dimension to ones understanding of mathematical concepts and graphing complex numbers is no exception. This video shows to graph complex numbers on the complex plane and what the results of adding complex...\n
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\n\"Complex\n\n
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\nComplex Numbers and Transformations\n

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\nYour 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...\n
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\n\"An\n\n
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\nEngageNY\n
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\nAn Appearance of Complex Numbers 1\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nComplex 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...\n
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Instructional Video5:05
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\n\"How\n\n
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\nHow Do You Graph Complex Numbers?\n

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\n\nFor Teachers\n\n10th - 11th\n
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\nComplex numbers have two parts and can be graphed on a complex plane. After an explanation of the complex plane, this video shows three examples of graphing complex numbers.\n
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\n\"Complex\n\n
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\nComplex Numbers\n

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\nIn this algebra worksheet, 11th graders solve complex numbers using division. multiplication, addition and subtraction. There are 11 questions with an answer key.\n
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\n\"Exploiting\n\n
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\nEngageNY\n
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\nExploiting the Connection to Cartesian Coordinates\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nMultiplication 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...\n
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\n\"The\n\n
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\nThe Geometric Effect of Some Complex Arithmetic 1\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nTranslating complex numbers is as simple as adding 1, 2, 3. In the ninth lesson plan 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...\n
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\n\"Two\n\n
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\nShodor Education Foundation\n
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\nTwo Variable Function Pump\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nUse a function to operate on two variables. Pupils look at operating with complex numbers as a function of two variables. The interactive squares the input and adds a constant to it. Learners visualize the resulting output and its...\n
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\n\"Plots\n\n
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\nCK-12 Foundation\n
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\nPlots of Polar Coordinates: Submarine Sonar\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nFind the location of enemy submarines with a sonar display that doubles as a polar coordinate system. Pupils find polar coordinates that would be the same location of plotted submarines. They then determine multiple polar...\n
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Instructional Video3:24
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\n\"Introduction\n\n
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\nIntroduction to Polar Coordinates - Concept\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nLearning polar coordinates does not require visiting the North Pole, though explaining igloos is much easier using polar coordinates. The lesson begins with a video explaining how to find coordinates on a spherical plane and how to...\n
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\n\"Discovering\n\n
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\nEngageNY\n
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\nDiscovering the Geometric Effect of Complex Multiplication\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nDoes 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...\n
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\n\"Matrix\n\n
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\nEngageNY\n
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\nMatrix Multiplication Is Not Commutative\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nShould 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...\n
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\n\"Complex\n\n
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\nComplex Analysis: Polar & Exponential Forms\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this polar and exponential form worksheet, students use Euler's Formula to write complex numbers in exponential form. They write numbers in rectangular form. This two-page worksheet contains seven multi-step problems.\n
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\n\"Complex\n\n
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\nComplex Analysis: Polar Form\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn 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...\n
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\n\"Justifying\n\n
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\nJustifying the Geometric Effect of Complex Multiplication\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nThe 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...\n
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\n\"Representing\n\n
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\nRepresenting Reflections with Transformations\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nIn 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...\n
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Instructional Video3:03
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\n\"Why\n\n
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\nWhy Is It Called a Square Root?\n

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\n\nFor Students\n\n7th - 10th\n\nStandards\n
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\nTake a radical look at square roots. The presentation examines square roots as the lengths of the sides of a square with a given area on the coordinate plane. Using this method, it is clear why the square root of a number can be positive...\n
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Assessment
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\nMt. San Antonio Collage\n
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\nQuiz 2: Types of Functions\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nHere is a resource that provides the structure of an assessment with the convenience of a full answer key. The focus is on rational, exponential, and logarithm functions with a few questions on solving polynomials. \n
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