Skip to the content

Math 2.0

Field theory and polynomials Object

Imaginary unit

Description

The imaginary unit is the complex number $i = 0 + 1 i$ . It satisfies $i^2 = -1$ , see i squared is minus one. It is a solution of the equation $x^2 + 1 = 0$ . The other solution is $-i$ . In the complex plane, $i$ is the point $(0, 1)$ , at distance $1$ above $0$ .

Remarks

The powers of $i$ repeat with period $4$ : $i^0 = 1$ , $i^1 = i$ , $i^2 = -1$ , $i^3 = -i$ and $i^4 = 1$ . Multiplication by $i$ turns the complex plane by a quarter turn about $0$ , counterclockwise. In electrical engineering, people often write $j$ for $i$ .

Where this leads

4 pages build on this one.

Further reading

Web https://en.wikipedia.org/wiki/Imaginary_unit, Definition
Web https://en.wikipedia.org/wiki/Imaginary_unit, Integer powers

About this page

Tag	`0ESCX36MMC`
URI	`m2://0ESCX36MMC`
Aliases	`i`
Kind	object
Writing	W1 stated
MSC	12D99
Same as	Wikidata Q193796 Wikipedia Imaginary unit

Markdown · JSON · Edit on GitHub

What this page needs for W2

section Invariants: a table of the main invariants (0 of 1)
edge instance_of out (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

Used by

i squared is minus one