# Algebra II : Basic Operations with Complex Numbers

## Example Questions

### Example Question #4681 : Algebra Ii

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 #1 : Understanding Imaginary And Complex Numbers

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 #4 : 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 #1 : 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 #61 : Imaginary Numbers

Find .

Explanation:

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

Reduce/simplify.

### Example Question #6 : How To Add Integers

Subtract:

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 #21 : Sat Subject Test In Math I

Multiply:

Answer must be in standard form.

Explanation:

The first step is to distribute which gives us:

which is in standard form.

### Example Question #1 : 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 #31 : Number Lines And Absolute Value

Divide:

The answer must be in standard form.