newRPL: The complexity of complex mode

[Vtile]

I think we just reached the point where we need the Hyperreal numbers and Non-standard calculus to calculate inf/inf? Which I found from wikipedia after your last post and find them really interesting and intuitive or atleast interesting.

Ok, lets forget that for now on.

This goes offtopic I think.

It seems I still get definition that says that ATan(inf/inf)=Pi/4 which is not defined (ie. in wolfram alpha), yet \( \mathit{z}=\infty*e^{\frac{i\pi}{4}}\) seems to be legit.

This is what I have found most formal definition for complex number.
\(\mathbb{C}=\left \{ \mathit{z} |\mathit{z=a+bi,\:\: a,b\in \mathbb{R}} ,\:\: i^2=-1 \right \} \)
also from a few sources that when Im(z)=0 then the result is real number.
Also it is said that infinity is part of the real number continuum and
calculation rule for complex number is given that
z1*z2=(a1,b1)(a2,b2)=(a1a2-b1b2 , a1b2+b1a2) then
\(\mathit{z}_{\infty }=\infty(a,b)=(\infty,0)(a,b)=(\infty*a-0*b \; ,\; \infty*b+0*a)=(\infty*a \; ,\; \infty*b)=(\infty \; ,\; \infty) = \left |\infty \right |\angle \frac{\pi }{2}=\left |\infty \right |e^{\frac{\pi}{2} i}\)


..Back to topic.
Yes, I thought the number system through the formal definition in the "rectangular form" \(\mathbb{C}=\left \{ \mathit{z} |\mathit{z=a+bi,\:\: a,b\in \mathbb{R}} ,\:\: i^2=-1 \right \} \) In the end the lossy representation is always the one that is not the one which is used through analysis.
I also didn't consider enough the \(\mathit{z}_{\infty }=\infty(a,b) \; and \; \infty \in \mathbb{R}\) (with the rule of )and using the Eulers Formula as \(\mathit{z}_{\infty }=\infty(Cos(\theta),Sin(\theta))\)

Interesting discussion, broadens ones thinking.

What comes to the mathematical environment, you said it yourself I just reworded it.