SAT Math : Complex Numbers

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #211 : Exponents

Raise  to the fourth power.

Possible Answers:

None of these

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:

Therefore, 

 

Example Question #41 : Complex Numbers

Raise  to the third power.

Possible Answers:

None of these

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 #221 : Exponents

Evaluate: 

Possible Answers:

The expression is undefined

Correct answer:

Explanation:

 is defined to be equal to  for any real or imaginary  and for any real ; therefore,

To evaluate a positive power of , divide the power by 4 and note the remainder:

Therefore, 

Substituting,

Rationalizing the denominator by multiplying both numerator and denominator by :

 

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