### All SAT II Math I Resources

## Example Questions

### Example Question #3 : Complex 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 #4 : Complex 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 #5 : Complex 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 #1 : Imaginary Numbers & Complex Functions

Simplify:

**Possible Answers:**

**Correct answer:**

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

Remember that , so .

Substitute in for

### Example Question #2 : Imaginary Numbers & Complex Functions

Simplify:

**Possible Answers:**

**Correct answer:**

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

Remember that , so .

Substitute in for

### Example Question #3 : Imaginary Numbers & Complex Functions

Simplify:

**Possible Answers:**

**Correct answer:**

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

Remember that , so .

Substitute in for

### Example Question #11 : Number Theory

Simplify:

**Possible Answers:**

**Correct answer:**

Remember that , so .

Substitute in for .

### Example Question #3 : Complex Conjugates

Simplify:

**Possible Answers:**

**Correct answer:**

To get rid of the fraction, multiply the numerator and denominator by the conjugate of the denominator.

Now, multiply and simplify.

Remember that

### Example Question #12 : Number Theory

Write in standard form:

**Possible Answers:**

None of the other answers

**Correct answer:**

Multiply by the conjugate:

### Example Question #9 : Imaginary Numbers

Simplify the expression.

**Possible Answers:**

None of the other answer choices are correct.

**Correct answer:**

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

Substitute to eliminate .

Simplify.

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