Standard - N-CN.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.

Standard - N-CN.2:
Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Standard - N-CN.3:
Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Standard - 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.

Standard - 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 + √3 i)3 = 8 because (-1 + √3 i) has modulus 2 and argument 120°.

Standard - 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.

Standard - N-CN.7:
Solve quadratic equations with real coefficients that have complex solutions.

Standard - N-CN.8:
Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x - 2i).

Standard - N-CN.9:
Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.