# Magnitude

Pronunciation: /ˈmæg.nɪˌtud/ Explain

The magnitude of a point in a coordinate system is the distance of that point from zero. For real numbers, the magnitude is also called the absolute value. Magnitude (and absolute value) are written using a vertical line '|'.

The magnitude of x is written |x|. The magnitude of -7 is written |-7|. Figure 1: Number line showing that 3 and -3 are both a distance of 3 from zero.

The number line in figure 1 shows that both the numbers 3 and -3 are a distance of 3 from zero.

#### Vectors

The magnitude of a vector is . Example: The magnitude of < -3, 4 > is calculated using the distance formula: .

#### Complex Numbers

The definition of magnitude is given as the distance of a number from zero. For complex numbers, the definition holds. Use the distance formula , where a is the length of one leg from zero and b is the length of the other leg from zero.

Take the complex number 4+3i. Figure 2 shows what this point looks like when plotted on the complex plain. Figure 2: The complex number 4 + 3i plotted on the complex plane

We can also use the distance formula to calculate the magnitude of 4+3i: We can write this in an equation as |4 + 3i| = 5.

Note that magnitude is always positive or zero. It can never be negative.

1. McAdams, David E.. All Math Words Dictionary, magnitude. 2nd Classroom edition 20150108-4799968. pg 112. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Fine, Henry B., Ph. D.. Number-System of Algebra Treated Theoretically and Historically. 2nd edition. www.archive.org. pp 28-51. Last Accessed 9/2/2018. http://www.archive.org/stream/thenumbersystemo17920gut/17920-pdf#page/n37/mode/1up/search/modulus. Buy the book

McAdams, David E. Magnitude. 4/24/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/m/magnitude.html.

### Revision History

4/24/2019: Changed equations and expressions to new format. (McAdams, David E.)
3/23/2019: Clarified magnitude of a vector. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
9/2/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)