'i' is not the square root of negative one. The square root of negative one is undefined, as the square root operation cannot be applied to numbers less than zero.

'i' is defined as a number with the property

i ² = -1

Calling it imaginary and saying it's the square root of negative one really annoyed profs at the University of Waterloo, who clearly needed to get out more often.

Also, i (or j if you prefer) is equal to exp(i*pi/2). This is easily derived from Euler's formula: exp(i*theta) = cos(theta) + i*sin(theta).

i as a variable of choice for traversing arrays

i, typically lower case, is typically used to traverse arrays in most of the computer programming languages in use today. Most notably C. And because of syntactical and learning curve relations, also C++, and Java.

Although various other variable names like - 'index'. 'counter', 'count' etc. are also invariably used, but even in projects with most well followed coding guidelines (which normally forbid defining any variable with name containing less than three characters), programmers feel comfortable only when using 'i' as an array subscript.

For multidimensional arrays or for two array traversals, 'j', 'k' 'l' etc. are commonly used.

This, it should be noted, is not without a reason.

The reasons for such uses are historical and date back to the times when FORTRAN was the language of a real programmer.

In FORTRAN, (specially the original one) one never needed to declare any variables, any variable with name starting with alphabets between (and including) 'I' and 'N' were integers by default. Similar alphabetical limits were defined for floats etc.

Thus, a programmer requiring an integer would typically start from 'I' and go on.

As most of initial C language programmers were proficient in Fortran, they naturally started by using 'i', 'j', 'k' etc. as the variables of choice for traversing the arrays.

• 1 in Roman numerals.
• 10 in the Greek number system.
• The most common word in conversational English.
• In electrical engineering, it's the letter used to represent the amount of current.

i is:

• The square root of -1, which is an imaginary number.
• The unit vector on the X axis, on a graphic.
• The most common variable used in for loops (or iteration in general).

It's also worth noting that the small dot over the i is called a tittle.

What is i?

I don't want to get into this horrible, difficult question right now. One time I was teaching a group of precocious young fiends who asked me this question over and over until I had to hide under my desk. There they surrounded me, and all I could do was plead with them that i was that peculiar thing that multiplies and adds just like other numbers (associatively, commutatively, and distributively), but when you square it the answer is -1. But they all just shrieked back at me, "That doesn't tell us what i is at all!"--except for one little monster who just kept screaming, "Why?" Just when I had decided to dash my brains out against the underside of the desk, the principal of the school walked in and swiftly settled the matter. "Look," he said, casting an authoritative glance about the room, "Mr. Smith's answer may not have addressed your question, but it has told you all you need to know in order to get the right answers on the Exam, and that is all Mr. Smith is here for--to tell you how to get the right answers on the Exam. Any questions that do not pertain to getting the right answers on the Exam, you can ask me in my office, after school hours. But you will please not bother Mr. Smith anymore with it." He then lifted me from under the desk, installed me back at the podium, whispered something encouraging in my ear, and left the classroom. I felt a bit shaky through the rest of the period, but at least the kids had shut up. --As should you.

I (i).

1.

I, the ninth letter of the English alphabet, takes its form from the Phenician, through the Latin and the Greek. The Phenician letter was probably of Egyptian origin. Its original value was nearly the same as that of the Italian I, or long e as in mete. Etymologically I is most closely related to e, y, j, g; as in dint, dent, beverage, L. bibere; E. kin, AS. cynn; E. thin, AS. ynne; E. dominion, donjon, dungeon.

See Guide to Pronunciation, §§ 98-106.

The dot which we place over the small or lower case i dates only from the 14th century. The sounds of I and J were originally represented by the same character, and even after the introduction of the form J into English dictionaries, words containing these letters were, till a comparatively recent time, classed together.

2.

In our old authors, I was often used for ay (or aye), yes, which is pronounced nearly like it.

3.

As a numeral, I stands for 1, II for 2, etc.

© Webster 1913.

I (?), pron. [poss. My (?) or Mine (); object. Me (?). pl. nom. We (); poss. Our (?) or Ours (); object. Us (?).] [OE. i, ich, ic, AS. ic; akin to OS. & D. ik, OHG. ih, G. ich, Icel. ek, Dan. jeg, Sw. jag, Goth. ik, OSlav. az', Russ. ia, W. i, L. ego, Gr. , , Skr. aham. &root;179. Cf. Egoism.]

The nominative case of the pronoun of the first person; the word with which a speaker or writer denotes himself.

© Webster 1913.