Editing Imaginary unit (section)

=== Imaginary integers and imaginary numbers ===

When the imaginary unit is repeatedly added or subtracted, the result is some [[integer]] times the imaginary unit, an ''imaginary integer''; any such numbers can be added and the result is also an imaginary integer:

<math display=block>ai + bi = (a + b)i.</math>

Thus, the imaginary unit is the generator of a [[group (mathematics)|group]] under addition, specifically an infinite [[cyclic group]].

The imaginary unit can also be multiplied by any arbitrary [[real number]] to form an [[imaginary number]]. These numbers can be pictured on a [[number line]], the ''imaginary axis'', which as part of the complex plane is typically drawn with a vertical orientation, perpendicular to the real axis which is drawn horizontally.