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## Adding and Subtracting Complex Numbers

#### High School - HSN-CN.A.2

How to Add, Subtract, and Multiply Complex Numbers Complex and imaginary numbers are one of the abstract topics in algebra. Most students struggle with this topic, as the name of the topic implies that it doesn't exist and have to be imagined. But working with complex numbers is not as complex as it might seem. Before we apply mathematical operations on the complex numbers, let us briefly recall what they are. When you take a square root of a negative number, you get an imaginary number. We use ‘i' to represent the imaginary number. And when we add the imaginary number to the real number, we get a complex number. We use a+bi to represent a complex number, where a denotes the real number and b denotes the imaginary part. ADDING COMPLEX NUMBERS - Adding two complex numbers is as easy is adding two real numbers. Consider two complex numbers (3-2i) and (-5-4i). now, combine the like terms, i.e., adding real numbers together and adding imaginary parts together. That means, {3+(-5) + (-2i)+(-4i)}, (-2 -6i) The general formula for adding complex numbers is written is, (a+bi) + (c+di) becomes (a+c) + (b+d)i SUBTRACTING COMPLEX NUMBERS - Subtraction is the same as the addition of complex numbers; you just have to more careful with the negative signs. Consider two complex numbers (-2+4i) and (3-i). now combine the like terms i.e., writing real numbers together and imaginary numbers together. {(-2-3) – (4i-(-i))}, (-5+5i) The general formula for subtraction of complex numbers is written as, (a+bi) – (c+di) becomes (a-c) + (b-d)i MULTIPLYING COMPLEX NUMBERS - Remember that when multiplying complex numbers, we use the properties that are applied in performing multiplication with real numbers Consider we are multiplying 2i with (3-8i) We will multiply 2i with each of term written within parentheses: 2i(3-8i), 2i(3) – 2i(8i), 6i-16i2, We know that i2= -1. Substituting the value: 6i – 16(-1), 6i+16

### Printable Worksheets And Lessons  #### Homework Sheets

Two sheets dedicated to sums and one sheet (#2) dedicated to differences.

• Homework 1 - Group the real part of the complex number and the imaginary part of the complex number.
• Homework 2 - The key is starting with the like terms.
• Homework 3 - Put it all together here.

#### Practice Worksheets

These are great for independent work all the answers are broken down for them.

• Practice 1 - Simplify the following: (12 – 24i) – (14 – 7i)
• Practice 2 - (21 – 42i) – (18 – 9i)
• Practice 3 - Combine the like terms and simplify.

#### Math Skill Quizzes

Each quiz is successively more difficult.

• Quiz 1 - The radicals make their way here.
• Quiz 2 - Do you best with this one.
• Quiz 3 - Start by understanding all the components that are present.