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 become infinitely large in a calculation. 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 also runs from −∞ to +∞.
Example 1
The hyperbolic tangent of an imaginary number can be converted to the tangent with
For the special value ½πi you get