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High School Algebra I: Help and Review25 chapters | 292 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, you will learn a simple way of thinking about magnitude and how to find it. You will also explore the differences in magnitude for simple numbers and complex numbers.

Just as the magnitude of an earthquake tells you how big the earthquake is, the **magnitude** of a mathematical term tells you how big that term is. In math, this means how far away the math term is from zero.

For numbers such as 1, 2, 3, and so on, the magnitude is simply the number itself. If the number is negative, the magnitude becomes the absolute value of the number. For example, the magnitude of 10 is 10. The magnitude of -10 becomes the absolute value of -10, which is 10. In both cases, the magnitude is the distance the mathematical term is from zero. Both 10 and -10 are a distance of 10 away from zero.

Here is a visual to help you picture it. This image shows us that the magnitude of both 10 and -10 is 10 because both are a distance 10 away from zero.

The process to find the magnitude of simple numbers requires only one step. This step is to take the absolute value of the number. For simple numbers, you can think of the **absolute value** as the positive version of every number. This is the only time in math where you can ignore the negative sign. When you are dealing with magnitude and absolute value, negative signs get dropped. Negative numbers are always positive in the world of magnitude and absolute value.

For example, the magnitude of 3.14 will always be 3.14 because the absolute value of a positive number is always itself. The magnitude of -3.14 will be 3.14 as well because the absolute value of a negative number is the positive version of the number without the negative sign. You are essentially dropping or ignoring the negative sign.

But remember, negative signs are very important in math everywhere else. Only when you are dealing with the absolute value of simple numbers can you ignore it.

**Complex numbers** have more than one part to them. Complex numbers are written with a '+' in between a real and an imaginary part. An example of a complex number is 4 + 3*i'. Notice that the complex number has two parts to it, a real and imaginary part, separated by a '+' sign. *

*Vectors are similar to imaginary numbers but are written differently. Vectors are usually graphed and are written inside a pair of parentheses with a comma separating each part. For example, a vector that points from the origin to the point (1 , 2) on a graph is written as (1 , 2). Notice that the vector form has two components to it, an *x

*Because complex numbers have more than one part, the process to find the magnitude requires a two-step process. Don't worry. There is a simple and easy-to-remember formula for you to use. The formula is the square root of the sum of each part squared. Written out, it looks like this: *

*It looks more intimidating than it actually is. All you actually have to do is square each part of the complex number, add the results, and take the square root of the result. This example will help you: *

*Notice how the formula is used similarly for both imaginary numbers and vectors. For each type, the separate parts are squared and then added. Then, the square root of the sum gives you the magnitude. Try it out for yourself with different numbers for each part. It's okay to use your calculator for this, but remember your order of operations. *

In summary, **magnitude** is the measurement of how large a mathematical term is. For **simple numbers**, it is the absolute value of the number. For **complex numbers**, a simple formula is used to calculate the magnitude. This formula is the square root of the sum of the parts squared.

Once you are done, you should be able to:

- Recall what the magnitude of a number is in math
- Explain how to find the magnitude of simple and complex numbers
- State the formula for finding the magnitude of a complex number

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High School Algebra I: Help and Review25 chapters | 292 lessons

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