Search the California Content Standards

Cluster:
Perform arithmetic operations with complex numbers.

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.

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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. [Polynomials 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. [Polynomials 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. [Polynomials with real coefficients; apply N.CN.9 to higher degree polynomials.]

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(+) Extend polynomial identities to the complex numbers.

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Use complex numbers in polynomial identities and equations. [Polynomials with real coefficients; apply N.CN.9 to higher degree polynomials.]

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

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Use complex numbers in polynomial identities and equations. [Polynomials 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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Understand independence and conditional probability and use them to interpret data.

Standard:
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). *

Cluster:
Understand independence and conditional probability and use them to interpret data.

Standard:
Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. *

Cluster:
Understand independence and conditional probability and use them to interpret data.

Standard:
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. *