SSAT Upper Level Math : How to graph complex numbers

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

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Example Question #1 : How To Graph Complex Numbers

Multiply:

Possible Answers:

Correct answer:

Explanation:

FOIL the product out:

Example Question #2 : How To Graph Complex Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

Use the square of a binomial pattern to multiply this:

Example Question #3 : How To Graph Complex Numbers

Multiply:

Possible Answers:

Correct answer:

Explanation:

This is a product of an imaginary number and its complex conjugate, so it can be evaluated using this formula:

Example Question #4 : How To Graph Complex Numbers

Multiply:

Possible Answers:

Correct answer:

Explanation:

This is a product of an imaginary number and its complex conjugate, so it can be evaluated using this formula:

Example Question #5 : How To Graph Complex Numbers

Define an operation  as follows:

For all complex numbers ,

Evaluate 

Possible Answers:

Correct answer:

Explanation:

Example Question #6 : How To Graph Complex Numbers

Define an operation  as follows:

For all complex numbers ,

Evaluate 

Possible Answers:

Correct answer:

Explanation:

Example Question #7 : How To Graph Complex Numbers

Evaluate .

Possible Answers:

The expression is undefined.

Correct answer:

Explanation:

Example Question #8 : How To Graph Complex Numbers

Define an operation  as follows:

For all complex numbers ,

Evaluate 

Possible Answers:

Correct answer:

Explanation:

Multiply both numerator and denominator by the conjugate of the denominator, , to rationalize the denominator:

Example Question #9 : How To Graph Complex Numbers

Define an operation  as follows:

For all complex numbers ,

Evaluate .

Possible Answers:

None of the other choices gives the correct answer.

Correct answer:

Explanation:

Example Question #10 : How To Graph Complex Numbers

Define an operation  as follows:

For all complex numbers ,

If  and , evaluate .

Possible Answers:

Correct answer:

Explanation:

If , then 

Distribute out  to yield

Either  or . However, we are given that , so 

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