SAT Math : How to add complex numbers

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #4 : Complex Numbers

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Rewrite  in their imaginary terms.

Example Question #3 : Complex Numbers

Add  and its complex conjugate.

Possible Answers:

Correct answer:

Explanation:

The complex conjugate of a complex number  is . Therefore, the complex conjugate of  is ; add them by adding real parts and adding imaginary parts, as follows:

,

the correct response.

Example Question #5 : Complex Numbers

Add  to its complex conjugate.

Possible Answers:

Correct answer:

Explanation:

The complex conjugate of a complex number  is . Therefore, the complex conjugate of  is ; add them by adding real parts and adding imaginary parts, as follows:

Example Question #3 : Complex Numbers

An arithmetic sequence begins as follows:

Give the next term of the sequence 

Possible Answers:

Correct answer:

Explanation:

The common difference  of an arithmetic sequence can be found by subtracting the first term from the second:

Add this to the second term to obtain the desired third term:

.

Example Question #6 : Complex Numbers

Simplify: 

Possible Answers:

Correct answer:

Explanation:

It can be easier to line real and imaginary parts vertically to keep things organized, but in essence, combine like terms (where 'like' here means real or imaginary):

Example Question #4 : Complex Numbers

For , what is the sum of  and its complex conjugate?

Possible Answers:

Correct answer:

Explanation:

The complex conjugate of a complex number  is , so  has  as its complex conjugate. The sum of the two numbers is

Example Question #7 : Complex Numbers

Evaluate: 

Possible Answers:

None of these

Correct answer:

Explanation:

A power of  can be evaluated by dividing the exponent by 4 and noting the remainder. The power is determined according to the following table:

, so 

, so 

, so 

, so 

Substituting:

Collect real and imaginary terms:

Example Question #11 : Complex Numbers

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

A power of  can be evaluated by dividing the exponent by 4 and noting the remainder. The power is determined according to the following table:

, so 

, so 

, so 

, so 

Substituting: 

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