{"id":7121,"date":"2012-03-15T10:17:19","date_gmt":"2012-03-15T02:17:19","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=7121"},"modified":"2012-03-15T10:38:10","modified_gmt":"2012-03-15T02:38:10","slug":"modulus-or-absolute-value-of-a-complex-number","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/mathematics\/modulus-or-absolute-value-of-a-complex-number-7121","title":{"rendered":"Modulus or absolute value of a complex number?"},"content":{"rendered":"

On my Polar Form of a Complex Number<\/a> page in IntMath, I state:<\/p>\n

\n

For the complex number x + yj<\/em> = r<\/em>(cos θ + j<\/em> sin θ), r<\/em> is the absolute value<\/strong> (or modulus<\/strong>) of the complex number.<\/p>\n<\/blockquote>\n

Reader Sunshine from the Philippines challenged this statement by saying:<\/p>\n

\n

absolute value doesn't have the same definition as modulus<\/p>\n<\/blockquote>\n

I enjoy such feedback because it makes me think more deeply about how I have written the definitions (or perhaps notation) on the site. We need to be clear, precise, and accurate, while making it understandable.<\/p>\n

So, is Sunshine correct?<\/h2>\n

This was my response to her.<\/p>\n

\n

In the case of complex numbers, the terms are generally interchangeable, but I agree this could be sloppy.<\/p>\n

These other math resources also use both terms for the same thing:<\/p>\n

Cut-The-Knot's Complex Numbers<\/a> <\/p>\n

Wikipedia's Absolute Value<\/a><\/p>\n

Mathwords' absolute value of a Complex Number<\/a> <\/p>\n

However, Pauls Online Notes<\/a> (Lamar University) makes some distinction between modulus of a complex number and absolute value of a real number (the latter is a degenerative case of the former). <\/p>\n

But in the sense that \"absolute value\" means distance from the origin for a real number (on the one-dimensional number line), and \"modulus\" means distance from the origin for a complex number (on the 2-dimensional complex plane), I don't believe there is a big problem with the interchangeability of the terms. The concept is certainly the same and it doesn't lead to a great deal of confusion.<\/p>\n

I would probably not write \"the absolute value of a complex number\" - it's certainly less common, and prefer \"the modulus of a complex number\".<\/p>\n

Thanks for triggering me to think about it!<\/p>\n<\/blockquote>\n

Readers, what are your thoughts on this? What does your text-book, or lecture notes say?<\/p>\n

See the 6 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"

\"Modulus<\/a>
\nA reader challenges me to define modulus of a complex number more carefully.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[4],"tags":[],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/7121"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=7121"}],"version-history":[{"count":0,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/7121\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=7121"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=7121"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=7121"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}