Again, you will see that we have located our imaginary units in real towns.

It is sometimes possible to identify the presence of an imaginary unit in a physical equation.

In particular, the square of the imaginary unit is 1:

They called this number i, or the imaginary unit.

This reflects the fact that also solves the equation - see imaginary unit.

Here is the Jones vector ( is the imaginary unit with ).

For a history of the imaginary unit, see Complex number: History.

Note the following identities for the imaginary unit and its reciprocal:

Above, complex numbers have been defined by introducing i, the imaginary unit, as a symbol.

The mathematical definition of an imaginary unit is , which has the property .

There are actually seven such maximal orders, one corresponding to each of the seven imaginary units.

In these expressions i is the imaginary unit.

(above, is the imaginary unit and is the Euclidean norm).

Well-known positional number systems for the complex numbers include the following ( being the imaginary unit):

The atomic number of the element is 'i', the Imaginary unit since the element does not exist.

The formula is important because it connects complex numbers ('i' stands for the imaginary unit) and trigonometric function.

(fundamental property of the imaginary unit).

The coordinates w, x, y, z are complex numbers with imaginary unit h:

Complex number arithmetic is generally supported by allowing the imaginary unit () in expressions and following all of its algebraic rules.

(Here, i is the imaginary unit and the well-known Dirac operator.)

Here, the imaginary unit is the (four-dimensional) volume element, and is the unit vector in time direction.

In the equation, j is the imaginary unit, and ω is the angular frequency of the wave.

Any complex number may be written a + bi, where a and b are real numbers and i is the imaginary unit.

The preceding definition of multiplication of general complex numbers follows naturally from this fundamental property of the imaginary unit.

The resemblance to the imaginary unit is not accidental: the subspace is R-algebra isomorphic to the complex numbers.