N. Number and Quantity
- G-GPE, N-RN, F-TF Coordinates of equilateral triangles
- N-RN, 8-NS Calculating the square root of 2
- N-RN Rational or Irrational?
N-RN.A. Extend the properties of exponents to rational exponents.
N-RN.A.1. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define $5^{1/3}$ to be the cube root of $5$ because we want $(5^{1/3})^3 = 5^{(1/3)3}$ to hold, so $(5^{1/3})^3$ must equal $5$.
N-RN.A.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
N-RN.B. Use properties of rational and irrational numbers.
N-RN.B.3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
N-Q.A. Reason quantitatively and use units to solve problems.
N-Q.A.1. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
N-Q.A.2. Define appropriate quantities for the purpose of descriptive modeling.
N-Q.A.3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
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N-CN.A. Perform arithmetic operations with complex numbers.
N-CN.A.1. Know there is a complex number $i$ such that $i^2 = -1$, and every complex number has the form $a + bi$ with $a$ and $b$ real.
N-CN.A.2. Use the relation $i^2 = -1$ and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
N-CN.A.3. Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
N-CN.B. Represent complex numbers and their operations on the complex plane.
N-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.
N-CN.B.5. Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, $(-1 + \sqrt{3} i)^3 = 8$ because $(-1 + \sqrt3 i)$ has modulus $2$ and argument $120^\circ$.
N-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.
N-CN.C. Use complex numbers in polynomial identities and equations.
N-CN.C.7. Solve quadratic equations with real coefficients that have complex solutions.
N-CN.C.8. Extend polynomial identities to the complex numbers. For example, rewrite $x^2 + 4$ as $(x + 2i)(x - 2i)$.
N-CN.C.9. Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
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