High School Math : Imaginary Numbers

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #41 : Algebra Ii

Simplify the following complex number expression:

Possible Answers:

Correct answer:

Explanation:

Begin by simplifying the radicals using complex numbers:

 

Multiply the factors:

Simplify. Remember that  is equivalent to .

Example Question #42 : Algebra Ii

Simplify the following complex number expression:

Possible Answers:

Correct answer:

Explanation:

Begin by completing the square:

 

Multiply the factors:

 

Simplify. Remember that  is equivalent to .

Example Question #43 : Algebra Ii

Simplify the following complex number expression:

Possible Answers:

Correct answer:

Explanation:

Begin by completing the square:

 

Now, multiply the factors:

 

Simplify. Remember that  is equivalent to .

 

Example Question #44 : Algebra Ii

Simplify the following complex number expression:

Possible Answers:

Correct answer:

Explanation:

Use the FOIL (First, Outer, Inner, Last) to multiply the complex numbers:

Combine like terms and simplify. Remember that  is equivalent to .

Example Question #45 : Algebra Ii

Simplify the following complex number expression:

Possible Answers:

Correct answer:

Explanation:

Begin by multiplying the numerator and denominator by the conjugate of the denominator:

 

Combine like terms:

Simplify. Remember that  is equivalent to .

Example Question #46 : Algebra Ii

Simplify the following complex number expression:

Possible Answers:

Correct answer:

Explanation:

Begin by multiplying the numerator and denominator by the conjugate of the denominator:

Combine like terms:

Simplify. Remember that  is equivalent to .

Example Question #47 : Algebra Ii

Simplify the following expression: 

Possible Answers:

Correct answer:

Explanation:

Simplifying expressions with complex numbers uses exactly the same process as simplifying expressings with one variable. In this case,  behaves similarly to any other variable. Thus, we have: 

Example Question #48 : Algebra Ii

Simplify the following complex number expression:

Possible Answers:

Correct answer:

Explanation:

Use the FOIL (First, Outer, Inner, Last) method to expand the expression:

Simplify. Remember that  is equivalent to .

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