Algebra II : Complex Imaginary Numbers

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #41 : Complex Imaginary Numbers

Simplify, if possible:   

Possible Answers:

Correct answer:

Explanation:

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

Expand the top and bottom.

Recall that:

 

Replace the imaginary term for .

Simplify this fraction.

The answer is:  

Example Question #42 : Complex Imaginary Numbers

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

Identify the least common denominator of the imaginary terms by using the FOIL method.

Simplify the terms.  Recall that:  

 and 

The expression becomes:

Convert the fractions of the original problem.

Simplify the numerators.

Replace the  term.

Replace the denominator with the value of the LCD.

Factor out a negative one.

Simplify by multiplying both the top and bottom by the conjugate of the denominator.  Factor both the top and bottom using the FOIL method.

Replace the  term.

Simplify the fraction.

The answer is:  

Example Question #42 : Complex Imaginary Numbers

Simplify:  

Possible Answers:

Correct answer:

Explanation:

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

Since the i-terms are imaginary numbers, write out the actual value of  and .

Simplify both top and bottom by the FOIL method.

Divide the two terms.

The answer is:  

Example Question #43 : Complex Imaginary Numbers

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Multiply 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 expression becomes:  

Recall that  and .  Replace the values.

The answer is:  

Example Question #45 : Complex Imaginary Numbers

Simplify, if possible:  

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 by FOIL method.  Recall that:   and .

Start with the numerator.

Solve the denominator.

Divide the numerator and denominator.

The answer is:  

Example Question #41 : Complex Imaginary Numbers

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Write out the power terms of .

Then,

Replace the terms.

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

Simplify both terms by the FOIL method.

Divide the numerator by the denominator.

The answer is:  

Example Question #42 : Complex Imaginary Numbers

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

Simplify the numerator.  Recall that  and .

Replace the value of .

Rewrite the fraction and split it into two terms.

Simplify both terms.

To simplify , multiply  on the top and bottom.

This means that:  

The answer is:  

Example Question #41 : Complex Imaginary Numbers

Solve:  

Possible Answers:

Correct answer:

Explanation:

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

Simplify the top and bottom.

The fraction becomes:  

Recall that  since .  Replace the value.

The answer is:  

Example Question #41 : Complex Imaginary Numbers

Possible Answers:

None of these.

Correct answer:

Explanation:

FOIL:

Simplify like terms:

Simplify :

Example Question #42 : Complex Imaginary Numbers

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Use the FOIL method to simplify the denominator.

The imaginary term is defined as:  

This means that:  

Replace the term.

The answer is:  

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