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Topic: The Complex Number System 

Common Core Mathematics 9-12

 Cluster  Perform arithmetic operations with complex numbers.
  Grade 9-12
   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.
   N.CN.2.Use the relation i2 = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
   N.CN.3.(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
 Cluster  Represent complex numbers and their operations on the complex plane.
  Grade 9-12
   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.
   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 + √ 3i)3 = 8 because (-1 + √ 3i) has modulus 2 and argument 120°.
   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.
 Cluster  Use complex numbers in polynomial identities and equations.
  Grade 9-12
   N.CN.7.Solve quadratic equations with real coefficients that have complex solutions.
   N.CN.8.(+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x − 2i).
   N.CN.9.(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.