College Algebra : College Algebra

Study concepts, example questions & explanations for College Algebra

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Example Questions

Example Question #17 : Complex Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal. 

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of -1+9i

Example Question #18 : Complex Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal. 

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 10-4i

Example Question #21 : Complex Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal. 

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of -8+9i

Example Question #132 : Review And Other Topics

Simplify:

Possible Answers:

Correct answer:

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal. 

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 9-5i

Example Question #23 : Complex Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal. 

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 9+9i

Example Question #24 : Complex Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal. 

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 18-i

Example Question #22 : Complex Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal. 

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 4-i

Example Question #417 : College Algebra

Rewrite in standard form:

Possible Answers:

None of these

Correct answer:

Explanation:

Multiply ply by the conjugate:

Simplify:

Example Question #418 : College Algebra

Rewrite in standard form:

Possible Answers:

None of these

Correct answer:

Explanation:

Find a common denominator and subtract.

To do so multiply the numerator and denominator of both fractions by the denominator of the opposite fraction:

Combine and simplify:

 

Keep in mind 

Example Question #1 : Solving Equations And Inequallities

Give all real solutions of the following equation:

Possible Answers:

Correct answer:

Explanation:

By substituting  - and, subsequently,  this can be rewritten as a quadratic equation, and solved as such:

We are looking to factor the quadratic expression as , replacing the two question marks with integers with product  and sum 5; these integers are .

Substitute back:

The first factor cannot be factored further. The second factor, however, can itself be factored as the difference of squares:

Set each factor to zero and solve:

 

Since no real number squared is equal to a negative number, no real solution presents itself here. 

 

The solution set is .

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