Algebra II : Complex Imaginary Numbers

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #31 : Imaginary Numbers

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Multiply the top and bottom by the conjugate of the denominator.

Multiply the numerator with the numerator.  Use the FOIL method.

Recall that , which indicates that .

Multiply the denominator with the denominator.

Divide the numerator with the denominator.

The answer is:  

Example Question #31 : Complex Imaginary Numbers

Solve:  

Possible Answers:

Correct answer:

Explanation:

In order to simplify this expression, we will need to multiply the numerator and denominator with the conjugate of the denominator.

Simplify the top and bottom.  The value of .

Divide the numerator with the denominator.

The answer is:  

Example Question #32 : Complex Imaginary Numbers

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and denominator by the conjugate of the denominator.

Simplify the top and the bottom.

Recall that , and .

This means that:

Re-substitute the actual values back into the fraction.

Reduce and split this fraction.

The correct answer is:  

Example Question #31 : Imaginary Numbers

Simplify:   

Possible Answers:

Correct answer:

Explanation:

The values are imaginary.  Recall that:

This means that:  

Rewrite the numerator.

Multiply the top and bottom by the conjugate of .

Rewrite the terms using the value of .

The answer is:  

Example Question #32 : Imaginary Numbers

Simplify:  

Possible Answers:

 

Correct answer:

 

Explanation:

In order to simplify this, we will need to multiply the top and bottom of the fraction by the conjugate of the denominator.

Multiply the numerator.

The term  since .  Replace the term and simplify.

Multiply the denominator.

The expression becomes:

Dividing the double negatives will result into a positive value.

The answer is:  

Example Question #31 : Imaginary Numbers

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Simplify the denominator.  Recall that , and .

Multiply the top and bottom by the conjugate of the denominator.  Use the FOIL method to simplify the denominator.

Replace the values of the known imaginary terms.

Simplify this fraction.

The answer is:  

Example Question #37 : Imaginary Numbers

Simplify:  

Possible Answers:

Correct answer:

Explanation:

In order to simplify this, we will need to multiply both the top and bottom by the conjugate of the denominator.

Simplify the top and bottom.  The bottom can be simplified by the FOIL method.

The value of  .  Replace the term.

Reduce this fraction.

The answer is:  

Example Question #38 : Imaginary Numbers

Simplify:  

Possible Answers:

Correct answer:

Explanation:

In order to simplify this expression, we will need to multiply the numerator and denominator by the conjugate of the denominator.

Simplify both the top and bottom.  Recall that:  

Divide the numerator with the denominator.

Simplify this term and split the fraction.

The answer is:  

Example Question #39 : Imaginary Numbers

Solve:  

Possible Answers:

Correct answer:

Explanation:

Multiply the top and bottom of the expression by the conjugate of the denominator.

Simplify the top and bottom using the FOIL method.

Note that:  

Replace the term.  The numerator becomes:

Simplify the denominator.

Divide the numerator with the denominator.

The answer is:  

Example Question #40 : Imaginary Numbers

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Multiply the top and bottom of this fraction by the conjugate of the denominator.

Simplify the numerator.  Recall that , and .

Simplify the denominator by FOIL method.

Divide the numerator with the denominator.

The answer is:  

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