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# High School: Number and Quantity: The Complex Number System

### HSN.CN.A.1

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.

### HSN.CN.A.2

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

### HSN.CN.A.3

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

### HSN.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.

### HSN.CN.B.5

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

### HSN.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.

### HSN.CN.C.7

Solve quadratic equations with real coefficients that have complex solutions.

### HSN.CN.C.8

Extend polynomial identities to the complex numbers.

### HSN.CN.C.9

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