PSAT Math : Complex Numbers

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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Example Question #1 : Complex Numbers

Simplify by rationalizing the denominator:

Possible Answers:

Correct answer:

Explanation:

Multiply both numerator and denominator by :

Example Question #1 : Complex Numbers

Divide:

Possible Answers:

Correct answer:

Explanation:

Rewrite in fraction form, and multiply both numerator and denominator by :

 

Example Question #71 : Exponents

Simplify by rationalizing the denominator:

Possible Answers:

Correct answer:

Explanation:

Multiply both numerator and denominator by :

Example Question #4 : Complex Numbers

Simplify by rationalizing the denominator:

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is :

 

Example Question #5 : Complex Numbers

Simplify by rationalizing the denominator:

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is :

Example Question #6 : Complex Numbers

Simplify by rationalizing the denominator:

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is :

Example Question #71 : Exponents

Define an operation  as follows:

For all complex numbers ,

.

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is . The above becomes:

Example Question #1 : How To Divide Complex Numbers

Define an operation  as follows:

For all complex numbers ,

.

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Example Question #9 : Complex Numbers

Define an operation  as follows:

For all complex numbers ,

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is . The above becomes:

Example Question #1 : Complex Numbers

Which of the following is equal to ?

Possible Answers:

None of the other responses is correct.

Correct answer:

Explanation:

By the power of a product property, 

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