MGSE9-12.N.VM.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., v, |v|, ||v||, v).

MGSE9-12.N.VM.2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

MGSE9-12.N.VM.3: Solve problems involving velocity and other quantities that can be represented by vectors.

MGSE9-12.N.VM.4 :Add and subtract vectors.

MGSE9-12.N.VM4a: 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.

MGSE9-12.N.VM4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

MGSE9-12.N.VM4c: Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, with the same magnitude as 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.

MGSE9-12.N.VM.5 :Multiply a vector by a scalar

MGSE9-12.N.VM.5a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).

MGSE9-12.N.VM.5b: Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v = 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

MGSE9-12.N.VM.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.

MGSE9-12.N.VM.4 :Add and subtract vectors.

MGSE9-12.N.VM4a: 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.

MGSE9-12.N.VM4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

MGSE9-12.N.VM4c: Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, with the same magnitude as 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.

MGSE9-12.N.VM.5 :Multiply a vector by a scalar

MGSE9-12.N.VM.5a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).

MGSE9-12.N.VM.5b: Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v = 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

MGSE9-12.N.VM.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.

• Dot Products
• Cross Products
• Angle Betweewn Vectors
  

MGSE9-12.N.CN.3:Find the conjugate of a complex number; use the conjugate to find the absolute value (modulus) and quotient of complex numbers.

MGSE9-12.N.CN.1 (Algebra 2): Understand there is a complex number i such that i^2= −1, and every complex number has the form a + bi where a and b are real numbers.

MGSE9-12.N.CN.2 (Algebra 2): Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

MGSE9-12.N.CN.3 (Algebra 2): Find the conjugate of a complex number; use the conjugate to find the absolute value (modulus) and quotient of complex numbers.

MGSE9-12.N.CN.3:Find the conjugate of a complex number; use the conjugate to find the absolute value (modulus) and quotient of complex numbers.

MGSE9-12.N.CN.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.

MGSE9-12.N.CN.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 + √3i)3 = 8 because (-1 + √3i) has modulus 2 and argument 120°.

MGSE9-12.N.CN.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.