N. Number and Quantity

    N-CN.A. Perform arithmetic operations with complex numbers.

      N-CN.A.3. Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

      • No tasks yet illustrate this standard.

    N-CN.B. Represent complex numbers and their operations on the complex plane.

      N-CN.B.4. Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

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      N-CN.B.5. Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, $(-1 + \sqrt{3} i)^3 = 8$ because $(-1 + \sqrt3 i)$ has modulus $2$ and argument $120^\circ$.

      N-CN.B.6. Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

    N-CN.C. Use complex numbers in polynomial identities and equations.

      N-CN.C.7. Solve quadratic equations with real coefficients that have complex solutions.

      N-CN.C.9. Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

      • No tasks yet illustrate this standard.

    N-VM.A. Represent and model with vector quantities.

      N-VM.A.1. Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., $\textbf{v}$, $|\textbf{v}|$, $||\textbf{v}||$, $v$).

      • No tasks yet illustrate this standard.

      N-VM.A.2. Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

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      N-VM.A.3. Solve problems involving velocity and other quantities that can be represented by vectors.

      • No tasks yet illustrate this standard.

    N-VM.B. Perform operations on vectors.

      N-VM.B.4. Add and subtract vectors.

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        N-VM.B.4.a. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

        • No tasks yet illustrate this standard.

        N-VM.B.4.b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

        • No tasks yet illustrate this standard.

        N-VM.B.4.c. Understand vector subtraction $\textbf{v} - \textbf{w}$ as $\textbf{v} + (-\textbf{w})$, where $-\textbf{w}$ is the additive inverse of $\textbf{w}$, with the same magnitude as $\textbf{w}$ and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

        • No tasks yet illustrate this standard.

      N-VM.B.5. Multiply a vector by a scalar.

      • No tasks yet illustrate this standard.

        N-VM.B.5.a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as $c(v_x, v_y) = (cv_x, cv_y)$.

        • No tasks yet illustrate this standard.

        N-VM.B.5.b. Compute the magnitude of a scalar multiple $c\textbf{v}$ using $||c\textbf{v}|| = |c|v$. Compute the direction of $c\textbf{v}$ knowing that when $|c|{v} \neq 0$, the direction of $c\textbf{v}$ is either along $\textbf{v}$ (for $c > 0$) or against $\textbf{v}$ (for $c < 0$).

        • No tasks yet illustrate this standard.

    N-VM.C. Perform operations on matrices and use matrices in applications.

      N-VM.C.6. Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

      • No tasks yet illustrate this standard.

      N-VM.C.7. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

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      N-VM.C.8. Add, subtract, and multiply matrices of appropriate dimensions.

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      N-VM.C.9. Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

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      N-VM.C.10. Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

      • No tasks yet illustrate this standard.

      N-VM.C.11. Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.

      • No tasks yet illustrate this standard.

      N-VM.C.12. Work with $2 \times2$ matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.

      • No tasks yet illustrate this standard.