{"id":6933,"date":"2025-05-03T00:01:20","date_gmt":"2025-05-03T07:01:20","guid":{"rendered":"https:\/\/c-for-dummies.com\/blog\/?p=6933"},"modified":"2025-06-03T21:52:21","modified_gmt":"2025-06-04T04:52:21","slug":"the-sqrt-1-0","status":"publish","type":"post","link":"https:\/\/c-for-dummies.com\/blog\/?p=6933","title":{"rendered":"The sqrt(-1.0)<\/em>"},"content":{"rendered":"

The four-letter word that made me avoid computers and programming for far too long is math<\/em>.
\n
\nI’m not good at math. Or I wasn’t good. But then I realized that computer programming isn’t just another complicated way to frustrate oneself with math. It’s different! This difference doesn’t mean, however, that programming and math never intersect. A case in point is the square root of -1.<\/p>\n

A square root is the inverse of a square. So 22<\/sup> = 4. And √4 = 2, which can also be written as 4½<\/sup> = 2.<\/p>\n

But what about -4? Which value when multiplied by itself equals -4? It can’t be -2, because -2 × -2 = 4; a negative value multiplied by a negative value is a positive value. Also, -2 × 2 are two different values.<\/p>\n

To avoid killing each other, mathematicians devised the constant i<\/em>, the imaginary unit. This value is defined as the square root of -1, or √-1. So, √-4 = 2i<\/em>. In the end, all the math works out well and the lives of thousands of mathematicians have been spared.<\/p>\n

But what about your C programs?<\/p>\n

Consider the following:<\/p>\n

2025_05_03-Lesson-a.c<\/a><\/h3>\n
\r\n#include <stdio.h>\r\n#include <math.h>\r\n\r\nint main()\r\n{\r\n    double i;\r\n\r\n    i = sqrt((double)-1.0);\r\n    printf(\"i = %f\\n\",i);\r\n\r\n    return 0;\r\n}<\/pre>\n
This code attempts to find the square root of -1.0. The sqrt()<\/em> function is called, which means you must link in the math library, -lm<\/code> when compiling this code at the command prompt in Linux.<\/p>\n
A printf()<\/em> statement outputs the result, stored in variable i<\/code>:<\/p>\n
i = -nan<\/code><\/p>\n
The value of variable i<\/code> is -nan<\/code>, or negative “not a number.” Darn.<\/p>\n
Not being one to give up, I tried a second approach with this code:<\/p>\n
2025_05_03-Lesson-b.c<\/a><\/h3>\n
\r\n#include <stdio.h>\r\n#include <math.h>\r\n\r\nint main()\r\n{\r\n    double i,x;\r\n\r\n    x = pow( sqrt((double)-1.0),(double)2.0);\r\n    printf(\"i^2 = %f\\n\",x);\r\n\r\n    return 0;\r\n}<\/pre>\n
The goal of this code is to raise -1 to the second power, to square -1. The result should be 1. Can the computer handle it?<\/p>\n
Here’s the output:<\/p>\n
i^2 = -nan<\/code><\/p>\n
Nope. Again, the result is negative not-a-number.<\/p>\n
In both cases, the computer is doing exactly what it’s told. As floating point values are (mostly) accurate, the result can’t be defined, so a nan<\/code> (not a number) exception is thrown. This condition doesn’t mean that all hope is lost.<\/p>\n
It’s entirely possible for the C compiler to handle complex numbers. I explain how in next week’s Lesson<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"
Can the C compiler calculate the square root of -1? Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-6933","post","type-post","status-publish","format-standard","hentry","category-main"],"_links":{"self":[{"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/6933","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6933"}],"version-history":[{"count":8,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/6933\/revisions"}],"predecessor-version":[{"id":7023,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/6933\/revisions\/7023"}],"wp:attachment":[{"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6933"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6933"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/c-for-dummies.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6933"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}