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Common Core: Standard
Common Core: ELA
Common Core: Math
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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 90degree rotations. Students use this...

 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....

 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.

 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...

 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...

 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...

 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.

 Student Outcomes Students derive the formula for zn = rn(cos(nθ) + i sin(nθ)) and use it to calculate powers of a complex number.

 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...

 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...

 Student Outcomes Students create a sequence of transformations that produce the geometric effect of reflection across a given line through the origin.

 Student Outcomes Students understand why the geometric transformation effect of the linear transformation L(z) = wz is dilation by w and rotation by the argument of w.

 Student Outcomes Students determine the geometric effects of transformations of the form L(z) = az, L(z) = (bi)z, and L(z) = (a+bi)z for real numbers a and b.

 Student Outcomes Students represent complex numbers in polar form and convert between rectangular and polar representations. Students explain why the rectangular and polar forms of a given complex...

 Student Outcomes Students apply distances between complex numbers and the midpoint of a segment. Students derive and apply a formula for finding the endpoint of a segment when given one endpoint and...

 Student Outcomes Students calculate distances between complex numbers as the modulus of the difference. Students calculate the midpoint of a segment as the average of the numbers at its endpoints.

 Student Outcomes Students represent multiplication of complex numbers geometrically on the complex plane.

 Student Outcomes Students represent addition, subtraction, and conjugation of complex numbers geometrically on the complex plane.

 In Topic B, students develop an understanding that when complex numbers are considered points in the Cartesian plane, complex number multiplication has the geometric effect of a rotation followed by...

 Student Outcomes Students determine the modulus and conjugate of a complex number. Students use the concept of conjugate to divide complex numbers.

 Student Outcomes Students determine the multiplicative inverse of a complex number. Students determine the conjugate of a complex number.

 Student Outcomes Students represent complex numbers as vectors. Students represent complex number addition and subtraction geometrically using vectors.

 Student Outcomes Students describe complex numbers and represent them as points in the complex plane. Students perform arithmetic with complex numbers, including addition, subtraction, scalar...

 Which Real Number Functions Define a Linear Transformation? Students develop facility with the properties that characterize linear transformations. Students learn that a mapping L:ℝ→ℝ is a linear...