# ACT Math : How to divide complex numbers

## Example Questions

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

Simplify:

Explanation:

Multiply both numberator and denominator by :

### Example Question #2331 : Act Math

Evaluate:

Explanation:

First, divide 100 by  as follows:

Now dvide this result by :

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

Evaluate:

Explanation:

First, divide 100 by  as follows:

Now, divide this by :

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

Evaluate:

Explanation:

First, evaluate :

Now divide this into :

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

Evaluate:

Explanation:

First, evaluate  using the square pattern:

Divide this into :

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

Complex numbers take the form , where  is the real term in the complex number and  is the nonreal (imaginary) term in the complex number.

Simplify:

Explanation:

This problem can be solved very similarly to a binomial such as . In this case, both the real and nonreal terms in the complex number are eligible to be divided by the real divisor.

, so

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

Complex numbers take the form , where  is the real term in the complex number and  is the nonreal (imaginary) term in the complex number.

Simplify by using conjugates:

Explanation:

Solving this problem using a conjugate is just like conjugating a binomial to simplify a denominator.

Multiply both terms by the denominator's conjugate.

Simplify. Note .

Combine and simplify.

Simplify the numerator.

The prime denominator prevents further simplifying.

Thus, .

Simplify: