Algebra II : Basic Operations with Complex Numbers

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1 : Basic Operations With Complex Numbers

What is the absolute value of 

Possible Answers:

Correct answer:

Explanation:

The absolute value is a measure of the distance of a point from the origin.  Using the pythagorean distance formula to calculate this distance.

Example Question #2 : Basic Operations With Complex Numbers

Consider the following definitions of imaginary numbers:

Then, 

Possible Answers:

Correct answer:

Explanation:

Example Question #3 : Basic Operations With Complex Numbers

Simplify the expression.

Possible Answers:

None of the other answer choices are correct.

Correct answer:

Explanation:

Combine like terms. Treat as if it were any other variable.

Substitute to eliminate .

Simplify.

Example Question #4 : Basic Operations With Complex Numbers

What is the value of ?

Possible Answers:

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 #5 : Basic Operations With Complex Numbers

What is the value of  ? 

Possible Answers:

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 #6 : Basic Operations With Complex Numbers

Find .

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and denominator by the numerator's complex conjugate.

Reduce/simplify.

Example Question #7 : Basic Operations With Complex Numbers

Subtract  from .

 

Possible Answers:

Correct answer:

Explanation:

This is essentially the following expression after translation:

Now add the real parts together for a sum of , and add the imaginary parts for a sum of .

Example Question #8 : Basic Operations With Complex Numbers

Multiply:

Answer must be in standard form.

Possible Answers:

Correct answer:

Explanation:

 The first step is to distribute which gives us:

  

which is in standard form.

Example Question #9 : Basic Operations With Complex Numbers

Add:

Possible Answers:

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 #10 : Basic Operations With Complex Numbers

Divide:

The 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  which results in

The numerator after simplification give us

The denominator is equal to 

Hence, the final answer in standard form =

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