### All PSAT Math Resources

## Example Questions

### Example Question #10 : Complex Numbers

Which of the following is equal to ?

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

By the power of a product property,

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

Multiply:

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

This is the product of a complex number and its complex conjugate. They can be multiplied using the pattern

with

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

Which of the following is equal to ?

**Possible Answers:**

**Correct answer:**

, so 56 is a multiple of 4. raised to the power of any multiple of 4 is equal to 1, so

.

### Example Question #3 : How To Multiply Complex Numbers

Which of the following is equal to ?

**Possible Answers:**

**Correct answer:**

The first step to solving this problem is distributing the exponent:

Next, we need simplify the complex portion.

Thus, our final answer is .

### Example Question #4 : How To Multiply Complex Numbers

What is the eighth power of ?

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

None of the other responses is correct.

raised to the power of any multiple of 4 is equal to 1, so the above expresion is equal to

This is not among the given choices.

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

What is the third power of ?

**Possible Answers:**

**Correct answer:**

You are being asked to evaluate

You can use the cube of a binomial pattern with :

### Example Question #6 : How To Multiply Complex Numbers

What is the fourth power of ?

**Possible Answers:**

**Correct answer:**

can be calculated by squaring , then squaring the result, using the square of a binomial pattern as follows:

### Example Question #7 : How To Multiply Complex Numbers

Multiply by its complex conjugate. What is the product?

**Possible Answers:**

**Correct answer:**

The product of any complex number and its complex conjugate is the real number , so all that is needed here is to evaluate the expression:

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

What is the eighth power of ?

**Possible Answers:**

The correct response is not given among the other choices.

**Correct answer:**

First, square using the square of a binomial pattern as follows:

Raising this number to the fourth power yields the correct response:

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

What is the ninth power of ?

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

To raise a negative number to an odd power, take the absolute value of the base to that power and give its opposite:

To raise to a power, divide the power by 4 and raise to the remainder. Since

,

Therefore,