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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.



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

tanh (ix) = i tan (x)

For the special value ½πi you get


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