According to definition of infinite tetration, this I*Omega has to a result of infinite tetration of a self root of type:
(I*Omega)^(1/(I*Omega)) = 8,619589667+I*13,42421553= e^(pi/2))^(1/Omega))*e^I
And that is true.
The angle of self root of I*Omega is (obvious from previous expression):
atan (13.42421553/8.619589667) = atan (1,557407725.) = 1 rad= 57,29577951 degrees.
And module is : 15,9532720360977
So the polar form of self root of I*Omega is:
(I*Omega)^(1/(I*Omega)) = 15,9532720360977*e^I = e^((pi/(2*Om))+I)
Taking a self root of a real number, in polar coordinates looks like as t increases, graph is tying a 1 loop knot, at same angle , whose tan= approx. 10,6 angle= 1,476 approx 84,6 degrees always. All self roots cross point where t=1 . What does a selfroot of complex number looks like I do not know. I do not have Complex function plotting software. Would be interesting to see z^(1/z) in 3D. The point I calculated has to be there as well, also i^(1/i)=e^(pi/2). Is it?
(I*Omega)^(1/(I*Omega)) = 8,619589667+I*13,42421553= e^(pi/2))^(1/Omega))*e^I
And that is true.
The angle of self root of I*Omega is (obvious from previous expression):
atan (13.42421553/8.619589667) = atan (1,557407725.) = 1 rad= 57,29577951 degrees.
And module is : 15,9532720360977
So the polar form of self root of I*Omega is:
(I*Omega)^(1/(I*Omega)) = 15,9532720360977*e^I = e^((pi/(2*Om))+I)
Taking a self root of a real number, in polar coordinates looks like as t increases, graph is tying a 1 loop knot, at same angle , whose tan= approx. 10,6 angle= 1,476 approx 84,6 degrees always. All self roots cross point where t=1 . What does a selfroot of complex number looks like I do not know. I do not have Complex function plotting software. Would be interesting to see z^(1/z) in 3D. The point I calculated has to be there as well, also i^(1/i)=e^(pi/2). Is it?