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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...
EngageNY
Trigonometry and Complex Numbers
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...
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...
EngageNY
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...
EngageNY
Discovering the Geometric Effect of Complex Multiplication
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...
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...
EngageNY
Comparing Data Distributions
Box in the similarities and differences. The 19th lesson in a unit of 22 presents class members with multiple box plots to compare. Learners use their understanding of five-number summaries and box plots to find similarities and...
National Institute of Open Schooling
Water Pollution
Fifteen million children under the age of five die each year due to diseases in their drinking water. Water pollution is the topic of lesson 34 in the series of 36. Scholars, through reading and discussing, study numerous aspects of...
National Institute of Open Schooling
Aldehydes, Ketones and Carboxylic Acids
Although their name makes them sound dangerous or toxic, carboxylic acids are found throughout nature in things such as citric acid, vinegar, and even in your DNA. Through detailed readings, discussions, and answering questions...
Messenger Education
Give Me a Boost—How Gravity Assists Aid Space Exploration
The propellant needed for space explorations runs in the thousands, while paying to get the craft into orbit costs millions! In the second installment of three, two activities explore laws of conservation of energy and momentum. Using...
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