PSAT Math : How to multiply complex numbers

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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Example Question #1 : How To Multiply 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, 

Example Question #2 : How To Multiply Complex Numbers

Multiply:

Possible Answers:

None of the other responses is correct.

Correct answer:

Explanation:

This is the product of a complex number and its complex conjugate. They can be multiplied using the pattern

with 

Example Question #3 : How To Multiply Complex Numbers

Which of the following is equal to  ?

Possible Answers:

Correct answer:

Explanation:

, so 56 is a multiple of 4.  raised to the power of any multiple of 4 is equal to 1, so

.

Example Question #4 : How To Multiply Complex Numbers

Which of the following is equal to ?

Possible Answers:

Correct answer:

Explanation:

The first step to solving this problem is distributing the exponent:

Next, we need simplify the complex portion.

Thus, our final answer is .

Example Question #5 : How To Multiply Complex Numbers

What is the eighth power of  ?

Possible Answers:

None of the other responses is correct.

Correct answer:

None of the other responses is correct.

Explanation:

 raised to the power of any multiple of 4 is equal to 1, so the above expresion is equal to 

This is not among the given choices.

Example Question #6 : How To Multiply Complex Numbers

What is the third power of  ?

Possible Answers:

Correct answer:

Explanation:

You are being asked to evaluate

You can use the cube of a binomial pattern with :

Example Question #7 : How To Multiply Complex Numbers

What is the fourth power of  ?

Possible Answers:

Correct answer:

Explanation:

 can be calculated by squaring , then squaring the result, using the square of a binomial pattern as follows:

 

 

Example Question #8 : How To Multiply Complex Numbers

Multiply  by its complex conjugate. What is the product?

Possible Answers:

Correct answer:

Explanation:

The product of any complex number  and its complex conjugate  is the real number , so all that is needed here is to evaluate the expression:

Example Question #9 : How To Multiply Complex Numbers

What is the eighth power of  ?

Possible Answers:

The correct response is not given among the other choices.

Correct answer:

Explanation:

First, square  using the square of a binomial pattern as follows:

 

 

Raising this number to the fourth power yields the correct response:

 

Example Question #10 : How To Multiply Complex Numbers

What is the ninth power of  ?

Possible Answers:

None of the other responses is correct.

Correct answer:

Explanation:

To raise a negative number to an odd power, take the absolute value of the base to that power and give its opposite:

To raise  to a power, divide the power by 4 and raise  to the remainder. Since 

,

Therefore, 

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