### All Algebra II Resources

## Example Questions

### Example Question #7 : Number Theory

**Possible Answers:**

**Correct answer:**

### Example Question #8 : Number Theory

Multiply:

**Possible Answers:**

**Correct answer:**

Use the FOIL technique:

### Example Question #9 : Number Theory

Evaluate:

**Possible Answers:**

**Correct answer:**

We can set in the cube of a binomial pattern:

### Example Question #1 : Irrational Numbers

Evaluate

**Possible Answers:**

You cannot divide by complex numbers

**Correct answer:**

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:

Our final answer is therefore

### Example Question #1 : Imaginary Numbers

Simplify the following product:

**Possible Answers:**

**Correct answer:**

Multiply these complex numbers out in the typical way:

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

which is our final answer.

### Example Question #2 : Imaginary Numbers

Identify the real part of

**Possible Answers:**

none of the above.

**Correct answer:**

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 #3 : Imaginary Numbers

Simplify:

**Possible Answers:**

**Correct answer:**

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

### Example Question #4 : Imaginary Numbers

Simplify:

**Possible Answers:**

**Correct answer:**

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

### Example Question #5 : Imaginary Numbers

Simplify:

**Possible Answers:**

**Correct answer:**

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

### Example Question #6 : Imaginary Numbers

Simplify:

**Possible Answers:**

**Correct answer:**

To subtract complex numbers, subtract the real terms together, then subtract the imaginary terms.

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