Algebra II : Complex Imaginary Numbers

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1 : Complex Imaginary Numbers

Possible Answers:

Correct answer:

Explanation:

Example Question #2 : Complex Imaginary Numbers

Multiply:

Possible Answers:

Correct answer:

Explanation:

Use the FOIL technique:

Example Question #2 : Number Theory

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

We can set  in the cube of a binomial pattern:

Example Question #3 : Complex 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 #2 : Imaginary Roots Of Negative Numbers

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 #1 : Complex 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 #5 : 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 add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.

Example Question #7 : 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 : Imaginary Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

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

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