# Algebra II : Complex Imaginary Numbers

## Example Questions

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Explanation:

### Example Question #2 : Irrational Numbers

Multiply:

Explanation:

Use the FOIL technique:

### Example Question #1 : Imaginary Numbers & Complex Functions

Evaluate:

Explanation:

We can set  in the cube of a binomial pattern:

### Example Question #1 : Complex Conjugates

Evaluate

You cannot divide by complex numbers

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:

### Example Question #2 : Irrational Numbers

Simplify the following product:

Explanation:

Multiply these complex numbers out in the typical way:

and recall that  by definition. Then, grouping like terms we get

### Example Question #1 : Complex Imaginary Numbers

Identify the real part of

none of the above.

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 #1 : Complex Imaginary Numbers

Simplify:

Explanation:

To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.

### Example Question #1 : Complex Imaginary Numbers

Simplify:

Explanation:

To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.

### Example Question #1 : Complex Imaginary Numbers

Simplify:

Explanation:

To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.

Simplify: