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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Use probability to evaluate outcomes of decisions. [Introductory; apply counting rules.]

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(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). *

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Use probability to evaluate outcomes of decisions. [Introductory; apply counting rules.]

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(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). *

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Calculate expected values and use them to solve problems.

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(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. *

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Calculate expected values and use them to solve problems.

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(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. *

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Calculate expected values and use them to solve problems.

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(+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.*