Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #73 : Imaginary Numbers

What is the value of , if = ?

 

 

Possible Answers:

Correct answer:

Explanation:

We know that . Therefore, . Thus, every exponent of  that is a multiple of 4 will yield the value of . This makes . Since , we know that .

Example Question #2 : Complex Numbers

Possible Answers:

The answer is not present.

Correct answer:

Explanation:

Combine like terms:

Distribute:

Combine like terms:

Example Question #13 : Basic Operations With Complex Numbers

Possible Answers:

Correct answer:

Explanation:

Example Question #5 : Complex Numbers

Rationalize the complex fraction: 

Possible Answers:

Correct answer:

Explanation:

To rationalize a complex fraction, multiply numerator and denominator by the conjugate of the denominator.

Example Question #5 : Complex Numbers

Rationalize the complex fraction: 

Possible Answers:

Correct answer:

Explanation:

To rationalize a complex fraction, multiply numerator and denominator by the conjugate of the denominator.

Example Question #2031 : Mathematical Relationships And Basic Graphs

Multiply:

Possible Answers:

Correct answer:

Explanation:

Distribute:

combine like terms:

 

Example Question #3 : Complex Numbers

Multiply: 

Possible Answers:

Correct answer:

Explanation:

Use FOIL to multiply the two binomials.

Recall that FOIL stands for Firsts, Outers, Inners, and Lasts.

Remember that 

Example Question #2032 : Mathematical Relationships And Basic Graphs

Simplify:

Possible Answers:

Correct answer:

Explanation:

Distribute the minus sign:

Combine like terms:

Example Question #21 : Basic Operations With Complex Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

Use FOIL to multiply the binomials:

Change  to -1:

Combine like terms:

Example Question #22 : Basic Operations With Complex Numbers

Find

Possible Answers:

Correct answer:

Explanation:

This pattern repeats every four powers. Divide the power by 4:

Since the remainder is 3, it is equivalent to , or .

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