## Conjugates and Dividing Complex Numbers

#### Aligned To Common Core Standard:

**High School** - HSN-CN.A.3

What is a Math Conjugate? Have you ever heard of the conjugate but couldn't fathom what it means? Let's teach you all on this one! The word conjugate is used in usually two contexts, in mathematics. One, when working with binomials which are half rational and half irrational numbers. Other times, a conjugate is used in the context when dealing with binomials which are again partially rational and partially imaginary. But normally, a math conjugate is when we change the middle sign of two like terms. For example: 3x + 1 It's conjugate is 3x - 1. Another example to further clarify the concept of a math conjugate; x + y it's conjugate is x - y. Here, we can say that x + y is a conjugate of x – y or x – y is the conjugate of x + y. In other words, two binomials could be the conjugates of each other.

### Printable Worksheets And Lessons

- Complex Quotients Step-by-step Lesson- When division isn't all about remainders or carrying the one.

- Guided Lesson - Find two conjugates and one quotient. A bit detailed though.

- Guided Lesson Explanation - I try to break it down into simple concepts for you.

- Practice Worksheet - Six conjugates and four quotients for you to work with.

- Matching Worksheet - Match the conjugates, quotients and the numbers that started it all off for you.

#### Homework Sheets

We start with finding the quotients of complex numbers. We finish off with determining conjugates.

- Homework 1 - To find conjugates remember,: The conjugate of a + bi = a – bi
- Homework 2 - Use the form we just learned in action.
- Homework 3 - Multiply the top and bottom by the conjugate.

#### Practice Worksheets

Time to work on some crazy division that you never thought was possible.

- Practice 1 - Determine the conjugate of the denominator.
- Practice 2 - Find the conjugates of: 5 + 25i
- Practice 3 - Do not forget to simplify at the end.

#### Math Skill Quizzes

Some of the questions work off of one another. See if that works for you.