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Common Core: Standard
Common Core: ELA
Common Core: Math
13 Results
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- Student Outcomes Students solve quadratic equations with complex solutions. Students understand the geometric origins of the imaginary unit i in terms of 90-degree rotations. Students use this...
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- Student Outcomes Students determine the complex roots of polynomial equations of the form xn = 1 and, more generally, equations of the form xn = k positive integers n and positive real numbers k....
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- Student Outcomes Students apply their understanding of polynomial identities that have been extended to the complex numbers to find the square roots of complex numbers.
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- Student Outcomes Students determine all solutions of polynomial equations over the set of complex numbers and understand the implications of the fundamental theorem of algebra, especially for...
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- Topic A brings students back to the study of complex roots of polynomial functions. Students briefly review quadratic and cubic functions and then extend familiar polynomial identities to both...
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- Student Outcomes Students interpret complex multiplication as the corresponding function of two real variables. Students calculate the amount of rotation and the scale factor of dilation in a...
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- Student Outcomes Students understand how a formula for the nth roots of a complex number is related to powers of a complex number. Students calculate the nth roots of a complex number.
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- Student Outcomes Students derive the formula for zn = rn(cos(nθ) + i sin(nθ)) and use it to calculate powers of a complex number.
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- Topic C highlights the effectiveness of changing notations and the power provided by certain notations such as matrices. The study of vectors and matrices is introduced through a coherent connection...
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- Student Outcomes Students apply their knowledge to understand that multiplication by the reciprocal provides the inverse geometric operation to a rotation and dilation. Students understand the...
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- Student Outcomes Students create a sequence of transformations that produce the geometric effect of reflection across a given line through the origin.
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- Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots...
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- Precalculus Module 1: Complex Numbers and Transformations Module 1 sets the stage for expanding students' understanding of transformations by exploring the notion of linearity. This leads to the...