### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #1 : How To Graph Complex Numbers

Multiply:

**Possible Answers:**

**Correct answer:**

FOIL the product out:

### Example Question #1 : How To Graph Complex Numbers

Simplify:

**Possible Answers:**

**Correct answer:**

Use the square of a binomial pattern to multiply this:

### Example Question #1 : How To Graph Complex Numbers

Multiply:

**Possible Answers:**

**Correct answer:**

This is a product of an imaginary number and its complex conjugate, so it can be evaluated using this formula:

### Example Question #1 : How To Graph Complex Numbers

Multiply:

**Possible Answers:**

**Correct answer:**

This is a product of an imaginary number and its complex conjugate, so it can be evaluated using this formula:

### Example Question #5 : How To Graph Complex Numbers

Define an operation as follows:

For all complex numbers ,

Evaluate

**Possible Answers:**

**Correct answer:**

### Example Question #1 : How To Graph Complex Numbers

Define an operation as follows:

For all complex numbers ,

Evaluate

**Possible Answers:**

**Correct answer:**

### Example Question #2 : How To Graph Complex Numbers

Evaluate .

**Possible Answers:**

The expression is undefined.

**Correct answer:**

### Example Question #8 : How To Graph Complex Numbers

Define an operation as follows:

For all complex numbers ,

Evaluate

**Possible Answers:**

**Correct answer:**

Multiply both numerator and denominator by the conjugate of the denominator, , to rationalize the denominator:

### Example Question #9 : How To Graph Complex Numbers

Define an operation as follows:

For all complex numbers ,

Evaluate .

**Possible Answers:**

None of the other choices gives the correct answer.

**Correct answer:**

### Example Question #10 : How To Graph Complex Numbers

Define an operation as follows:

For all complex numbers ,

If and , evaluate .

**Possible Answers:**

**Correct answer:**

If , then

.

Distribute out to yield

Either or . However, we are given that , so

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