# College Algebra : Complex Numbers

## Example Questions

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### Example Question #1 : Complex Numbers

Consider the following definitions of imaginary numbers:

Then,

Possible Answers:

Correct answer:

Explanation:

### Example Question #21 : Number Theory

What is the value of ?

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Correct answer:

Explanation:

When dealing with imaginary numbers, we multiply by foiling as we do with binomials. When we do this we get the expression below:

Since we know that  we get  which gives us

### Example Question #4 : Basic Operations With Complex Numbers

What is the value of  ?

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Correct answer:

Explanation:

Recall that the definition of imaginary numbers gives that  and thus that . Therefore, we can use Exponent Rules to write

### Example Question #9 : Basic Operations With Complex Numbers

Add:

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Correct answer:

Explanation:

When adding complex numbers, add the real parts and the imaginary parts separately to get another complex number in standard form.

Adding the real parts gives , and adding the imaginary parts gives .

### Example Question #5 : Basic Operations With Complex Numbers

Divide:

The answer must be in standard form.

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Correct answer:

Explanation:

Multiply both the numerator and the denominator by the conjugate of the denominator which is  which results in

The numerator after simplification give us

The denominator is equal to

Hence, the final answer in standard form =

### Example Question #1 : Complex Numbers

Divide:

Answer must be in standard form.

Possible Answers:

Correct answer:

Explanation:

Multiply both the numerator and the denominator by the conjugate of the denominator which is  resulting in

This is equal to

giving us .

### Example Question #2 : Complex Numbers

Evaluate:

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Correct answer:

Explanation:

Use the FOIL method to simplify. FOIL means to mulitply the first terms together, then multiply the outer terms together, then multiply the inner terms togethers, and lastly, mulitply the last terms together.

The imaginary  is equal to:

Write the terms for .

Replace  with the appropiate values and simplify.

### Example Question #3 : Complex Numbers

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The answer is not present.

Correct answer:

Explanation:

Combine like terms:

Distribute:

Combine like terms:

### Example Question #4 : Complex Numbers

Rationalize the complex fraction:

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Correct answer:

Explanation:

To rationalize a complex fraction, multiply numerator and denominator by the conjugate of the denominator.

### Example Question #5 : Complex Numbers

Multiply:

Possible Answers:

Correct answer:

Explanation:

Use FOIL to multiply the two binomials.

Recall that FOIL stands for Firsts, Outers, Inners, and Lasts.

Remember that

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