Search the California Content Standards

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

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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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Interpret the structure of expressions. [Polynomial and rational]

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Interpret expressions that represent a quantity in terms of its context. * Interpret parts of an expression, such as terms, factors, and coefficients. *

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Interpret the structure of expressions. [Polynomial and rational]

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Interpret expressions that represent a quantity in terms of its context. * Interpret complicated expressions by viewing one or more of their parts as a single entity. *

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Interpret the structure of expressions. [Polynomial and rational]

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Use the structure of an expression to identify ways to rewrite it.

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Write expressions in equivalent forms to solve problems.

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Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.*

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Translate between the geometric description and the equation for a conic section.

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Given a quadratic equation of the form ax^2 + by^2 + cx + dy + e = 0, use the method for completing the square to put the equation into standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola and graph the equation. [In Algebra II, this standard addresses only circles and parabolas.] CA