# Common Core: The Complex Number System

##### HSN.CN.A3

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

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.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.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.CN.C7

Solve quadratic equations with real coefficients that have complex solutions.

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##### HSN.CN.A1

Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real.

October 1, 2018##### HSN.CN.A2

Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

October 1, 2018