# Precalculus : Find the Quotient of Complex Numbers

## Example Questions

### Example Question #1 : Find The Quotient Of Complex Numbers

Let . Find a simple form of .

Explanation:

We remark first that:

and we know that :

.

This means that:

### Example Question #1 : Find The Quotient Of Complex Numbers

What is ?

Explanation:

Since ,

the problem becomes,

### Example Question #1 : Find The Quotient Of Complex Numbers

Write

in the form  for some real numbers  and

Explanation:

The correct answer is

Using simple algebra and multiplying the expression by the complex conjugate of the denominator, we get:

### Example Question #1 : Find The Quotient Of Complex Numbers

Divide:

Explanation:

To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator.

To find the conjugate, just change the sign in the denominator. The conjugate used will be .

Now, distribute and simplify.

Recall that

### Example Question #5 : Find The Quotient Of Complex Numbers

Divide:

Explanation:

To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator.

To find the conjugate, just change the sign in the denominator. The conjugate used will be .

Now, distribute and simplify.

Recall that

### Example Question #1 : Find The Quotient Of Complex Numbers

Divide.

Explanation:

To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator.

To find the conjugate, just change the sign in the denominator. The conjugate used will be .

Now, distribute and simplify.

Recall that

### Example Question #7 : Find The Quotient Of Complex Numbers

Divide.

Explanation:

To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator.

To find the conjugate, just change the sign in the denominator. The conjugate used will be .

Now, distribute and simplify.

Recall that

### Example Question #8 : Find The Quotient Of Complex Numbers

Divide.

Explanation:

To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator.

To find the conjugate, just change the sign in the denominator. The conjugate used will be .

Now, distribute and simplify.

Recall that

### Example Question #9 : Find The Quotient Of Complex Numbers

Divide.

Explanation:

To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator.

To find the conjugate, just change the sign in the denominator. The conjugate used will be .

Now, distribute and simplify.

Recall that

Divide.