# Multiplication of Complex Numbers Worksheets

Outside of division, this is one of the more complex operations that we can perform with complex numbers. The imaginary part always worries students, but the truth is that if you treat these expressions just like your standard binomial expressions that you are finding the product of, it is the same things. When you multiply you use the standard FOIL method that outlines of progression of calculating the product. In the end, we just need to combine all the like terms. These worksheets and lessons will help you better understand how to process multiplication between two complex numbers.

### Aligned Standard: HSN-CN.B.5

- Add and Subtract of Complex Numbers Step-by-step Lesson- We focus on understanding the sum and difference rules of complex numbers.
- Multiplication of Complex Numbers Lesson - I thought it best to separate the product in this lesson because it is a much different method than the others.
- Guided Lesson - We practice on every form of the standard.
- Guided Lesson Explanation - The steps you need to take to compete these problems are clear cut and straight forward.
- Practice Worksheet - Another ten problems that will help you work towards the mastery of this skill.
- Matching Worksheet - Match the complex numbers and their operations to their sum, product, or difference.
- Addition and Subtraction of Complex Numbers Five Pack - See if you can figure out the pattern that I fit in here.
- Multiplying and Dividing Complex Numbers Five Pack - Make no mistake there are more products than quotients in these.
- Absolute Value of Complex Numbers Five Pack - Some of these numbers are super complex.
- Addition and Subtraction of Complex Numbers Five Pack - A slight reverb of the first five pack, but it is a slight bit more sophisticated.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

More subtraction will be added soon.

- Homework 1 - These types of problems are not that challenging.
- Homework 2 - The formula for the product of two complex numbers is: (a+bi)(c+di) = a(c+di) + bi(c+di)
- Homework 3 - Combine and finish is the best method.

### Practice Worksheets

We focus on the use of the operations and the final outcome.

- Practice 1 - When you are adding complex numbers, you just combine like terms.
- Practice 2 - When subtracting, just do the reverse and subtract like terms.
- Practice 3 - The addition rule for complex numbers states: (m +ni) + (p + qi) = (m + p) + (n + q)i m an p are real numbers.

### Math Skill Quizzes

Can't be a good operation working sheet for complex numbers.

- Quiz 1 - ni and qi are the imaginary numbers.
- Quiz 2 - Place our numbers into this formula: (56 + 59i) + (66 + 89i)
- Quiz 3 - Start adding two brackets.

### How to Perform Basic Operations with Complex Numbers

Complex numbers are the combination of a real number and an imaginary number in the form: a + bi Here, a and b are the real numbers, whereas i is the imaginary number. As you will move up in grade levels, you will be faced with complex mathematics problems to solve. You will come across problems that will require you to perform operations on real and imaginary numbers together. In such a case, you would be required to write them in the form of a complex number to be able to add, subtract, multiply, or divide them. Follow these steps to perform basic mathematical operations on these complex numbers.

**Addition** - Add the like parts (terms), it is that simple. Add the real part of the complex number to the real part and the imaginary part to the imaginary part. You can simply consider the imaginary portion (i) a variable for all intents and purposes when you are processing operations.

**Subtraction** - To subtract them, make sure to arrange the real parts at one side and the imaginary to the other side, then perform subtraction. It follows the same type of format that we used for addition.

**Multiplication** - They appear as binomials and if you remember how we multiplied binomials previously, not much changes here. Use the FOIL method and multiple the first terms, then the outer terms, then the inner terms, ending with the last terms. You finish this off by just combining all the like terms to create your new expression.

**Division** - To perform division on two complex numbers, start by multiplying the numerator and denominator by the complex conjugate, then expand and simplify. After it is done, write the final answer in standard form.