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Algebra 2
▸
Polynomial arithmetic
•
Descartes's rule of signs
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Difficult factoring problems
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Polynomial long division and graphing cubics
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Rational root theorem
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Higher-order polynomials
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Remainder theorem
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Factor theorem
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Sum and difference of cubes
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Reciprocal polynomials
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Adding and subtracting polynomials
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Multiplying binomials by polynomials
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Proving the sum and difference of cubes formulas
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Factoring and solving polynomials by graphing
▸
Complex numbers
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Intro to complex numbers
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Powers of the imaginary unit
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Simplifying square roots of negative integers
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Plotting complex numbers
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Adding and subtracting complex numbers
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Multiplying complex numbers
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Complex number conjugates
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Dividing complex numbers
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Modulus and argument of a complex number
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Proving properties of the complex modulus
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Converting complex numbers between polar and rectangular form
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Powers of complex numbers using modulus and argument
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Square root of a complex number
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Distance and midpoint of complex numbers
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Linear factorization
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Solving equations with complex numbers
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Quadratic equations with complex solutions
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Complex conjugate root theorem
▸
Polynomial factorization, division, and end behavior
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Finding the GCD and LCM of polynomials
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Sophie Germain's identity
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Dividing a polynomial by a monomial
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Dividing quadratics by linear expressions
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Polynomial long division
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Synthetic division
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Converting improper algebraic fractions to mixed algebraic fractions
▸
Rational exponents and radicals
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Adding and subtracting radicals
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Converting between radicals and rational exponents
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Rewrite exponential expressions
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Simplifying expressions with radicals and rational exponents
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Solving equations with radicals and rational exponents
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Transformations of the square and cube root functions
▸
Logarithms
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Evaluating logarithms
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Evaluating natural logarithms
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Converting between logarithmic form and exponential form
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Evaluating logarithmic expressions using the one-to-one property
▸
Expanding and condensing logarithmic expressions
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Expanding logarithmic expressions
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Condensing logarithmic expressions
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Lesson
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Practice
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Inverses of exponential and logarithmic functions
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Graphing logarithmic functions
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Sketching logarithmic functions under transformations
▸
Properties of logarithms
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Intro
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Proofs
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Using the theorems
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Solving logarithmic inequalities
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Solving literal equations using properties of logarithms
▸
Solving logarithmic equations
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Solving logarithmic equations using the one-to-one property
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Solving logarithmic equations using the properties of logarithms
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Verifying logarithmic identities
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Fractal dimension
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Logarithmic scale
▸
Transformations of functions
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Shifting, scaling, and reflecting
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Even and odd functions
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Wishful thinking strategy
▸
Equations and inequalities
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Solving literal equations
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Alternative quadratic formula
▸
Solving exponential equations
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Solving exponential equations using the one-to-one property
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Lesson
•
Practice
•
Intersections of lines, circles, and parabolas
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Solving and graphing polynomial inequalities using a sign chart
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Solving and graphing rational inequalities using a sign chart
•
Direct variation
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Inverse variation
▸
Rational functions
•
Adding and subtracting rational expressions
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Finding the domain and range of rational functions
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Graphing rational functions
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Asymptotes and intercepts of rational functions
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Graphing reciprocal functions
•
Multiplying and dividing rational expressions
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Simplifying complex fractions with variables
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Simplifying rational expressions
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Simplifying square roots of rational expressions
•
Solving literal rational equations
•
Solving rational equations
›
Algebra 2
›
Complex numbers
›
Other resources
Graphing with complex numbers
Students will learn why
$$\lvert z_1z_2 \rvert = \lvert z_1 \rvert \lvert z_2 \rvert$$
To see a proof, you can read
this,
or watch
this.
YouTube videos
1045
Graphing with Complex Numbers (1 of 3: Initial algebraic expansion)
Eddie Woo
1046
Graphing with Complex Numbers (2 of 3: Determining the region)
Eddie Woo
1047
Graphing with Complex Numbers (3 of 3: Is |z₁z₂| equal to |z₁| × |z₂|?)
Eddie Woo
278949
Graphs in the Complex Plane (1 of 4: Introductory Examples)
Eddie Woo
278950
Graphs in the Complex Plane (2 of 4: Graphing Complex Inequalities)
Eddie Woo
278951
Graphs in the Complex Plane (3 of 4 : Shifting the Point of Reference)
Eddie Woo
278952
Graphs in the Complex Plane (4 of 4: Where is the argument measured from?)
Eddie Woo