# PSAT Math : Complex Numbers

## Example Questions

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### Example Question #1 : Complex Numbers

Simplify by rationalizing the denominator:

Explanation:

Multiply both numerator and denominator by :

### Example Question #1 : Complex Numbers

Divide:

Explanation:

Rewrite in fraction form, and multiply both numerator and denominator by :

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

Simplify by rationalizing the denominator:

Explanation:

Multiply both numerator and denominator by :

### Example Question #4 : Complex Numbers

Simplify by rationalizing the denominator:

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is :

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

Simplify by rationalizing the denominator:

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is :

### Example Question #6 : Complex Numbers

Simplify by rationalizing the denominator:

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is :

### Example Question #7 : Complex Numbers

Define an operation  as follows:

For all complex numbers ,

.

Evaluate .

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is . The above becomes:

### Example Question #1 : Complex Numbers

Define an operation  as follows:

For all complex numbers ,

.

Evaluate .

Explanation:

### Example Question #9 : Complex Numbers

Define an operation  as follows:

For all complex numbers ,

Evaluate .

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is . The above becomes:

### Example Question #2 : Complex Numbers

Which of the following is equal to ?