The Complex Number System
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Perform Arithmetic Operations With Complex Numbers.
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N.CN.1Know there is a complex number i suc…more
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.
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N.CN.2Use the relation i2 = –1 and the c…more
Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
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N.CN.3(+) Find the conjugate of a complex …more
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
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Represent Complex Numbers And Their Operations On The Complex Plane.
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N.CN.4(+) Represent complex numbers on the…more
(+) 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.
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N.CN.5(+) Represent addition, subtraction,…more
(+) 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°.
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N.CN.6(+) Calculate the distance between n…more
(+) 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.
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Use Complex Numbers In Polynomial Identities And Equations.
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N.CN.7Solve quadratic equations with real …more
Solve quadratic equations with real coefficients that have complex solutions.
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N.CN.8(+) Extend polynomial identities to …more
(+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
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N.CN.9(+) Know the Fundamental Theorem of …more
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
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