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Martin Sleziak
Martin Sleziak
6:54 AM
Since this was asked in another room and it is tag-related - just a reminder that a tag with no questions are automatically removed by a script that runs once a day. More details can be found here: meta.stackexchange.com/tags/tag-pruning/info
 
 
15 hours later…
Martin Sleziak
Martin Sleziak
10:22 PM
A new tag split-complex-numbers. The tag-creator also created the tag-excerpt and the tag-wiki.
1
Q: compute $\log_e(j)$ of split complex number $j$

HoloI am trying to calculate the value of $\ln j$ where $j^2=1, j\ne\pm1$($j$ is split complex). this is how i did it: given $e^{j\theta}=\cosh\theta+j\sinh\theta$ I can set $\cosh\theta=0\implies \theta = i\pi n - \frac{i \pi}2, n \in \Bbb Z,i$ is the imaginary number, for convenience sake i'll...

proof-verification logarithms split-complex-numbers
Split-complex number
In abstract algebra, a split complex number (or hyperbolic number, also perplex number, double number) has two real number components x and y, and is written z = x + y j , j 2 = + 1. {\displaystyle z=x+yj,\quad j^{2}=+1.} The conjugate of z is z* = x - y j. Since j2 = +1, z z ∗ = x ...
 

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