### Imaginary infinity

Mathematics has the concept of **imaginary infinity**. It is written as +∞* i* and −∞* i*.

First of all, we don't know what infinity is. That may sound strange, but there is nobody who really can imagine. Mathematicians don't care about that.

##### Explanation

A complex number can geometrically be represented by a point in the complexe plane. That consists of a real *x*-axis and orthogonal to that the imaginary *y*-axis. The *x*-axis runs from −∞ to +∞ and the *y*-axis from −∞ *i* to +∞ *i*.

##### Example 1

The hyperbolic tangent of an imaginary number can be converted to the tangent with

For the special value ½π*i* you get