# Simplifying Complex Numbers Worksheets

How to Simplify Complex Numbers? One of the most common forms of number systems that students have to deal with is the complex numbers. These are numbers that are a combination of imaginary and real numbers. Real numbers include all rational and irrational numbers. An imaginary number is any negative integer in square root. To add or subtract complex numbers, you identify the real and imaginary portion of the numbers and place the like terms together. Sum all numbers in the real portion and sum all numbers in the imaginary portion. You apply the same methodology when subtracting complex numbers. To multiply complex numbers, you need to understand the F.O.I.L rule. F.O.I.L stands from first, outer, inner, last. You have to multiply each term of the first binomial with each term in the second binomial. Start by multiplying the first term of a binomial with the first term of the second one, multiply the same term with the second term of the second binomial. The third step is to multiply the second term of the first binomial with both terms of the second binomial. Simplify the sum further to get the final answer. Division of complex numbers is rather complicated, as compared to multiplication, subtraction, or addition. Write the division in the form of a fraction and multiply both the numerator and the denominator with the conjugate of the denominator. The conjugate of a complex number a + ib is a - ib. It will help you convert the denominator from a complex number to a real number. These worksheets and lessons will show you how to simplify a series of complex numbers.

### Aligned Standard: HSN-CN.A.1

- Negative Radical Step-by-step Lesson- The first problem I saw totally reminded me that I forgot everything from my University Calculus classes.
- Guided Lesson - Sums of negative radicals, imaginary numbers, and simplifying negative radicals again.
- Guided Lesson Explanation - There is a good bit of diversity between these problems even though they come under the same math standard.
- Practice Worksheet - Two of these problems will leave you shaking your head for just a bit.
- Matching Worksheet - One more to see if you will rise to the challenge of complex numbers.
- Standard from Complex Numbers Five Pack - We have you restate these complex numbers in a whole different number of ways.
- Absolute Value of Complex Numbers Five Pack - This is pretty interesting. Most people either love or hate these problems.

- Answer Keys - These are for all the unlocked materials above.
- Homework 1 - You will simplify these operations as far down as you can.
- Homework 2 - Make sure that you pay attention to the presence of parathesis.
- Practice Worksheet 1 - You will use these problems to get a good understanding of more complex problems.
- Practice Worksheet 2 - We get one last chance to learn what ever we missed.
- Quiz 1 - A good time to assess where you sit with these skills.
- Quiz 2 - There are a mix of more complex and simple problems here. Good to see if students are paying attention.

### The General Steps to Simplifying Complex Numbers

When we are performing operations on complex numbers it seems a bit overwhelming, but if you just take a step back and remember that these are just value that need to be put together it feels more doable. Here are the basic steps we would suggest that you take when evaluating these types of problems:

** Add and Subtract** - This is an easy way to get rid or gain some imaginary units. For all intents at purposes, at this stage, you are combining them like any other variable. Also do not forget to combine all of the real numbers or constants.

**Multiplication Uses The FOIL Rule** - When you need to multiply a real and imaginary portion of two binomials. Remember that the FOIL (First, Outside, Inside, Last) applies to make sure that properly process the product of two binomials together. Remember that when you multiple a rational and irrational number together the product will be irrational. In the end you will combine all the like terms together to, in most cases, create a new polynomial.

**Division** - When you divide two complex numbers, write them just like you would a fraction. Once you do that find the conjugate of the denominator and multiple the numerator and denominator by that conjugate. From there you are just simplifying the terms to make them more amenable.