# 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 #2 : How To Divide Complex Numbers

Evaluate:

Explanation:

First, divide 100 by  as follows:

Now dvide this result by :

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

Evaluate:

Explanation:

First, divide 100 by  as follows:

Now, divide this by :

### Example Question #2 : 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 #33 : Squaring / Square Roots / Radicals

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 #3 : 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, .

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

Simplify:

Explanation:

This problem can be solved in a way similar to other kinds of division problems (with binomials, for example). We need to get the imaginary number out of the denominator, so we will multiply the denominator by its conjugate and multiply the top by it as well to preserve the number's value.

Then, recall  by definition, so we can simplify this further:

This is as far as we can simplify, so it is our final answer.