Search the California Content Standards

Cluster:
Perform arithmetic operations with complex numbers. [i^2 as highest power of i]

Standard:
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.

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Perform arithmetic operations with complex numbers. [i^2 as highest power of i]

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Use the relation i^2 = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

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Use complex numbers in polynomial identities and equations. [Quadratics with real coefficients]

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Solve quadratic equations with real coefficients that have complex solutions.

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Use complex numbers in polynomial identities and equations. [Quadratics with real coefficients]

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(+) Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).

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Use complex numbers in polynomial identities and equations. [Quadratics with real coefficients]

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(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

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Represent and solve equations and inequalities graphically. [Combine polynomial, rational, radical, absolute value, and exponential functions.]

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Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. *

Cluster:
Represent and solve equations and inequalities graphically. [Combine polynomial, rational, radical, absolute value, and exponential functions.]

Standard:
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. *

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Understand solving equations as a process of reasoning and explain the reasoning. [Simple radical and rational]

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Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

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Understand solving equations as a process of reasoning and explain the reasoning. [Simple radical and rational]

Standard:
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

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Solve equations and inequalities in one variable.

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Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context. CA