The coordinate system most frequently used to quantitatively describe a n-dimensional space.
In 2 dimensions, i.e. a plane, it describes any point as a function of 2 perpendicular unit vectors (1,0) and (0,1) and in 3 dimensions as a function of 3 perpendicular unit vectors (1,0,0), (0,1,0) and (0,0,1).
Functions in 2 dimensions are often conveniently described using the so-called theory of functions. When using this type of mathematical description, the
imaginary number
i = √(-1) is introduced to label the y-axis.
a + ib is then actually a 2 dimensional
vector with a x-axis component of 'a' and a y-axis component of 'b'.
The 'a' is called the
real part and the 'b' the
imaginary part of the function, an expression that is frequently encountered in
MRI, where the
real image is a pixel-wise representation of 'a' and the
imaginary image a pixel-wise representation of 'b', with 'a' and 'b' the components of the xy-
magnetization along the x- and y-axis, respectively.
(Renatus Cartesius/Rene Descartes, 1596-1650, French philosopher and mathematician)