SAT Math : How to multiply complex numbers

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #24 : Complex Numbers

Raise  to the power of 3.

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

Explanation:

To raise any expression  to the third power, use the pattern

Setting :

Taking advantage of the Power of a Product Rule:

Since ,

and

:

Collecting real and imaginary terms:

Example Question #31 : Complex Numbers

Evaluate .

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

Explanation:

Apply the Power of a Product Rule:

,

and

so, substituting and evaluating:

Example Question #32 : Complex Numbers

Raise  to the power of 4.

Possible Answers:

Correct answer:

Explanation:

The easiest way to find  is to note that  

.

Therefore, we can find the fourth power of  by squaring , then squaring the result.

Using the binomial square pattern to square :

Applying the Power of a Product Property:

Since  by definition: 

Square this using the same steps:

,

the correct response.

Example Question #31 : Complex Numbers

Evaluate 

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

None of the other choices gives the correct response.

Explanation:

Apply the Power of a Product Rule:

Applying the Product of Powers Rule:

 raised to any multiple of 4 is equal to 1, and , so, substituting and evaluating:

This is not among the given choices.

Example Question #44 : Squaring / Square Roots / Radicals

 is the complex conjugate of .

Evaluate 

.

Possible Answers:

Correct answer:

Explanation:

 conforms to the perfect square trinomial pattern

.

The easiest way to solve this problem is to add  and , then square the sum. 

The complex conjugate of a complex number  is .

,

so  is the complex conjugate of this; 

and 

Substitute 14 for :

.

Example Question #45 : Squaring / Square Roots / Radicals

 is the complex conjugate of .

Evaluate 

.

Possible Answers:

Correct answer:

Explanation:

 conforms to the perfect square trinomial pattern

.

The easiest way to solve this problem is to add  and , then square the sum. 

The complex conjugate of a complex number  is .

,

so  is the complex conjugate of this; 

and 

Substitute 8 for :

.

Example Question #46 : Squaring / Square Roots / Radicals

 is the complex conjugate of .

Evaluate 

.

Possible Answers:

Correct answer:

Explanation:

 conforms to the perfect square trinomial pattern

.

The easiest way to solve this problem is to subtract  and , then square the difference. 

The complex conjugate of a complex number  is .

,

so  is the complex conjugate of this; 

Substitute  for :

By definition, , so, substituting,

,

the correct choice.

Example Question #2401 : Sat Mathematics

Remember that .

Simplify: 

Possible Answers:

Correct answer:

Explanation:

Use FOIL to multiply complex numbers as follows:

Since , it follows that , so then:

Combining like terms gives:

Example Question #11 : How To Multiply Complex Numbers

Simplify: 

Possible Answers:

Correct answer:

Explanation:

Use FOIL:

Combine like terms:

But since , we know

Example Question #49 : Squaring / Square Roots / Radicals

 is the complex conjugate of .

Evaluate 

.

Possible Answers:

Correct answer:

Explanation:

 conforms to the perfect square trinomial pattern

.

The easiest way to solve this problem is to subtract  and , then square the difference. 

The complex conjugate of a complex number  is .

,

so  is the complex conjugate of this; 

Taking advantage of the Power of a Product Rule and the fact that :

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