What is Magnitude? - Definition & Concept

What is Magnitude? - Definition & Concept
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  • 0:05 What is Magnitude?
  • 1:01 Magnitude for Simple Numbers
  • 2:04 Magnitude for Complex Numbers
  • 3:47 Lesson Summary
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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.

What is Magnitude?

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.

magnitude

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.

How to Find the Magnitude for Simple Numbers

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.

How to Find the Magnitude for Complex Numbers

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 + 3i'. Notice that the complex number has two parts to it, a real and imaginary part, separated by a '+' sign.

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