PSAT Math : How to multiply complex numbers

Example Questions

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Example Question #1 : How To Multiply Complex Numbers

Which of the following is equal to ?

None of the other responses is correct.

Explanation:

By the power of a product property,

Example Question #1 : How To Multiply Complex Numbers

Multiply:

None of the other responses is correct.

Explanation:

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

with

Example Question #2 : How To Multiply Complex Numbers

Which of the following is equal to  ?

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 ?

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 #82 : Exponents

What is the eighth power of  ?

None of the other responses is correct.

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 #2 : How To Multiply Complex Numbers

What is the third power of  ?

Explanation:

You are being asked to evaluate

You can use the cube of a binomial pattern with :

Example Question #1 : How To Multiply Complex Numbers

What is the fourth power of  ?

Explanation:

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

Example Question #2 : How To Multiply Complex Numbers

Multiply  by its complex conjugate. What is the product?

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 #1 : How To Multiply Complex Numbers

What is the eighth power of  ?

The correct response is not given among the other choices.

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 #1 : How To Multiply Complex Numbers

What is the ninth power of  ?

None of the other responses is correct.