### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #11 : How To Graph Complex Numbers

Give the number which, when multiplied by , yields the same result as if it were increased by 6.

**Possible Answers:**

No such number exists.

**Correct answer:**

Let be the number in question. The statement "[a number] multiplied by yields the same result as if it were increased by 6" can be written as

We can solve this for as follows:

Rationalize the denominator by multiplying both numerator and denominator by the conjugate of the denominator, which is :

### Example Question #12 : How To Graph Complex Numbers

Define an operation as follows:

For all complex numbers ,

.

If , evaluate .

**Possible Answers:**

None of the other choices gives the correct answer.

**Correct answer:**

,

by our definition, can be rewritten as

or

Taking the reciprocal of both sides, then multiplying:

### Example Question #401 : Geometry

Raise to the power of 4.

**Possible Answers:**

The expression is undefined.

**Correct answer:**

### Example Question #14 : 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 #15 : How To Graph Complex Numbers

Give the number which, when added to 20, yields the same result as if it were subtracted from .

**Possible Answers:**

No such number exists.

**Correct answer:**

Let be the number in question. The statement "[a number] added to 20 yields the same result as if it were aubtracted from " can be written as

Solve for :

### Example Question #16 : 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 #17 : How To Graph Complex Numbers

Subtract from its complex conjugate. What is the result?

**Possible Answers:**

**Correct answer:**

The complex conjugate of a complex number is , so the complex conjugate of is . Subtract the former from the latter:

### Example Question #18 : How To Graph Complex Numbers

Give the product of and its complex conjugate.

**Possible Answers:**

The correct answer is not given among the other responses.

**Correct answer:**

The correct answer is not given among the other responses.

The product of a complex number and its conjugate is

which will always be a real number. Therefore, all four given choices, all of which are imaginary, can be immediately eliminated. The correct response is that the correct answer is not given among the other responses.

### Example Question #19 : How To Graph Complex Numbers

Add to its complex conjugate. What is the result?

**Possible Answers:**

**Correct answer:**

The complex conjugate of a complex number is , so has as its complex conjugate; the sum of the two numbers is

### Example Question #20 : How To Graph Complex Numbers

Multiply the complex conjugate of by . What is the result?

**Possible Answers:**

**Correct answer:**

The complex conjugate of a complex number is , so the complex conjugate of is . Multiply this by :