# Algebra II : Basic Operations with Complex Numbers

## Example Questions

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### Example Question #7 : Understanding Imaginary And Complex Numbers

What is the absolute value of

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 #1 : Basic Operations With Complex Numbers

Consider the following definitions of imaginary numbers:

Then,

Explanation:

### Example Question #17 : Sat Subject Test In Math I

Simplify the expression.

None of the other answer choices are correct.

Explanation:

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

Substitute to eliminate .

Simplify.

### Example Question #2 : Basic Operations With Complex Numbers

What is the value of ?

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 #3 : Basic Operations With Complex Numbers

What is the value of  ?

Explanation:

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

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

Find .

Explanation:

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

Reduce/simplify.

### Example Question #2 : How To Add Integers

Subtract  from .

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 #3 : How To Add Integers

Multiply:

Answer must be in standard form.

Explanation:

The first step is to distribute which gives us:

which is in standard form.

### Example Question #5 : How To Add Integers

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 #71 : Imaginary Numbers

Divide:

The answer must be in standard form.

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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