Perform operations on matrices and use matrices in applications.Compute the direction of cv knowing that when |c|v is not equal to 0, the direction of cv is either along v (for c > 0) or against v (for c < 0). .5b Compute the magnitude of a scalar multiple cv using ||cv|| = |c|..5a 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).Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. .4c 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..4b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. .4a Add vectors end-to-end, component-wise, and by the parallelogram rule..3 Solve problems involving velocity and other quantities that can be represented by vectors..2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v). .1 Recognize vector quantities as having both magnitude and direction.

Represent and model with vector quantities.

9-12.HSN-VM Vector and Matrix Quantities.

.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.

.5 Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane use properties of this representation for computation.

.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.

Represent complex numbers and their operations on the complex plane.

.3 Find the conjugate of a complex number use conjugates to find moduli and quotients of complex numbers.

Perform arithmetic operations with complex numbers.

Khan academy math precalculus