High School: Number and Quantity

HSN.CN.A3

(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

October 1, 2018
HSN.VM.B4

(+) Add and subtract vectors.

October 1, 2018
HSN.CN.B4

(+) 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.

October 1, 2018
HSN.VM.B4a

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.

October 1, 2018
HSN.CN.B5

(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3 i)3 = 8 because (-1 + √3 i) has modulus 2 and argument 120°.

October 1, 2018
HSN.VM.B4b

Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

October 1, 2018
HSN.CN.B6

(+) 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.

October 1, 2018
HSN.VM.B4c

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.

October 1, 2018
HSN.CN.C7

Solve quadratic equations with real coefficients that have complex solutions.

October 1, 2018
HSN.VM.B5

(+) Multiply a vector by a scalar.

October 1, 2018
HSN.CN.C8

(+) Extend polynomial identities to the complex numbers. For example, rewrite x² + 4 as (x + 2i)(x – 2i).

October 1, 2018
HSN.CN.C9

(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

October 1, 2018