Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #1 : Imaginary Numbers

Evaluate 

Possible Answers:

You cannot divide by complex numbers

Correct answer:

Explanation:

To divide by a complex number, we must transform the expression by multiplying it by the complex conjugate of the denominator over itself. In the problem,  is our denominator, so we will multiply the expression by  to obtain:

.

We can then combine like terms and rewrite all  terms as . Therefore, the expression becomes:

Our final answer is therefore 

Example Question #4621 : Algebra Ii

Simplify the following product:

Possible Answers:

Correct answer:

Explanation:

Multiply these complex numbers out in the typical way:

and recall that  by definition. Then, grouping like terms we get

which is our final answer.

Example Question #2 : Imaginary Numbers

Identify the real part of

Possible Answers:

none of the above.

Correct answer:

Explanation:

A complex number in its standard form is of the form: , where  stands for the real part and  stands for the imaginary part. The symbol  stands for .

The real part in this problem is 1.

Example Question #11 : Sat Subject Test In Math I

Simplify:

Possible Answers:

Correct answer:

Explanation:

To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.

Example Question #2 : Complex Imaginary Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.

Example Question #3 : Complex Imaginary Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.

Example Question #2 : Imaginary Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

To subtract complex numbers, subtract the real terms together, then subtract the imaginary terms.

Example Question #1 : Complex Imaginary Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

To subtract complex numbers, subtract the real terms, then subtract the imaginary terms.

Example Question #1961 : Mathematical Relationships And Basic Graphs

Simplify:

Possible Answers:

Correct answer:

Explanation:

To subtract complex numbers, subtract the real terms, then subtract the imaginary terms.

Example Question #2 : Imaginary Roots Of Negative Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

Remember that , so .

Substitute in  for 

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