### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #3 : Complex Imaginary 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 : 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 #14 : Number Theory

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 #31 : Number Lines And Absolute Value

Divide:

The answer must be in standard form.

**Possible Answers:**

**Correct answer:**

Multiply both the numerator and the denominator by the conjugate of the denominator which is which results in

The numerator after simplification give us

The denominator is equal to

Hence, the final answer in standard form =

### Example Question #1 : Complex Conjugates

**Possible Answers:**

**Correct answer:**

The definition of a complex conjugate is each of two complex numbers with the same real part and complex portions of opposite sign.

### Example Question #1 : Complex Conjugates

Which of the following is the complex conjugate of ?

**Possible Answers:**

**Correct answer:**

The complex conjugate of a complex equation is .

The complex conjugate when multiplied by the original expression will also give me a real answer.

The complex conjugate of is

### Example Question #1 : Complex Conjugates

Simplify

**Possible Answers:**

**Correct answer:**

In problems like this, you are expected to simplify by removing i from the denominator. To do this, multiply the numerator and denominator by the conjugate of the denominator (switch the sign between the two terms from either a plus to a minus or vice versa) over itself. The conjugate over itself equals 1 and does not change the value of the expression (any number multiplied by 1 is still that number). Multiplying by the conjugate is the only way to eliminate i since there will be no middle term when we foil.

Simplify i squared to -1 and then combine like terms

### Example Question #1 : Complex Conjugates

Simplify

**Possible Answers:**

**Correct answer:**

In problems like this, you are expected to simplify by removing i from the denominator. To do this, multiply the numerator and denominator by the conjugate of the denominator (switch the sign between the two terms from either a plus to a minus or vice versa) over itself. The conjugate over itself equals 1 and does not change the value of the expression (any number multiplied by 1 is still that number). Multiplying by the conjugate is the only way to eliminate i since there will be no middle term when we foil.

Simplify i squared to be -1 and then combine like terms

### Example Question #1 : Complex Conjugates

Simplify

**Possible Answers:**

**Correct answer:**

In problems like this, you are expected to simplify by removing i from the denominator. To do this, multiply the numerator and denominator by the conjugate of the denominator (switch the sign between the two terms from either a plus to a minus or vice versa) over itself. The conjugate over itself equals 1 and does not change the value of the expression (any number multiplied by 1 is still that number). Multiplying by the conjugate is the only way to eliminate i since there will be no middle term when we foil.

Simplify i squared to be -1 and then combine like terms

### Example Question #1 : Complex Conjugates

Simplify

**Possible Answers:**

**Correct answer:**

Simplify i squared to be -1 and then combine like terms

The coefficients of all the terms can divide by 4 so reduce each of them