imaginary unit
التعريفات والمعاني
== English ==
=== Etymology ===
So named because it takes on the role of unit for the imaginary part of a complex number.
=== Noun ===
imaginary unit (plural imaginary units)
(number theory, complex analysis, quaternion theory) An imaginary number (in the case of complex numbers, usually denoted
i
{\displaystyle i}
) that is defined as a solution to the equation
x
2
=
−
1
{\displaystyle x^{2}=-1}
.
2014, Dennis G. Zill, Warren S. Wright, Advanced Engineering Mathematics, Ascend Learning (Jones & Bartlett Learning), 5th Edition, page 793,
We now simply say that
i
{\displaystyle i}
is the imaginary unit and define it by the property
i
2
=
−
1
{\displaystyle i^{2}=-1}
. Using the imaginary unit, we build a general complex number out of two real numbers.
==== Usage notes ====
The imaginary unit of complex analysis is usually denoted
i
{\displaystyle i}
. In some fields (for instance, electrical engineering), however, it is customarily denoted
j
{\displaystyle j}
, to avoid confusion with the symbol for electric current.
The complex numbers are generated by assuming a single imaginary unit,
i
{\displaystyle i}
, and constructing the numbers
a
+
b
i
{\displaystyle a+bi}
, where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers.
The quaternions (regardable as an extension of the complex numbers) are similarly generated by assuming three distinct imaginary units,
i
,
j
,
k
{\displaystyle i,j,k}
, and constructing the numbers
a
+
b
i
+
c
j
+
d
k
{\displaystyle a+bi+cj+dk}
.
==== Translations ====