# PSAT Math : How to divide complex numbers

## Example Questions

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

Simplify by rationalizing the denominator:

Explanation:

Multiply both numerator and denominator by :

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

Divide:

Explanation:

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

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

Simplify by rationalizing the denominator:

Explanation:

Multiply both numerator and denominator by :

### Example Question #4 : 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 #5 : 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 : 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 #7 : How To Divide 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 #8 : How To Divide Complex Numbers

Define an operation  as follows:

For all complex numbers ,

.

Evaluate .

Explanation:

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

Define an operation  as follows:

For all complex numbers ,

Evaluate .