What is the Square Root of -1i?

LOL Surely someone saw THIS one coming. If 1i is the Square Root of -1, then what is the Square Root of -1i? It's time for a NEW Math system that accounts for such things...and we should invent it! Right here, right now!

Let me know what you think!

No mathematical impossibilities here. The square root of -i is sqrt(2)/2 * (1-i), or about 0.707*(1-i). The square root of any imaginary number is:



(image from Wolfram's MathWorld)

Notice that there are actually two values for the square root. I just gave the principal square root in my example.

[Edited on 5/31/2004 by PurdueNuc]

I thought math was discovered not invented.

PurdueNuc is right, as any good calculator will tell you. Mathworld also has another formula on their site.

First of all, I'm impressed with your patience and THANK YOU for writing out that formula for us. Second of all, you gotta read Flatland-The book.

Finally, we REALLY SHOULD modify our numbers scale. Why not start by having a numbers scale that runs NOT ONLY left to right (for positive and negative numbers) and up and down (for positive and negative Imaginary numbers) BUT ALSO vertically? In my mind's eye, it starts some where above the paper and goes down through the desk thus giving our scale a decidedly "three dimensional" effect.



What'cha think? We could call them Depth numbers (since the others already represent Height and Width) ...-3d,-2d,-1d, 0,1d,2d,3d...and so on.

Writing them out might be a problem...any suggestions?

[Edited on 1-6-2004 by Toelint]

It's still the holiday, so Math is a bit too much till tommorow, when the week starts.

Our number scale isnt definitive...
Unless a maths system describes everything in the universe, it isnt 'Gods maths' as such
The SQRT of -1 is only used because our maths system isnt good enough

We usually skip a number system with 3 dimensions to go directly to 4 or 8 dimensions. This is because only 1, 2, 4 and 8 dimensional number system are Division Algebra's. This means only in those four systems every non-zero number has a multiplicative inverse.

The number systems are:

• 1 dimension: Natural numbers
  
• 2 dimensions: Complex numbers (i)
  
• 4 dimensions: Quaternions (i, j and k)
  
• 8 dimensions: Octonions or Cayley numbers (e0 to e7)
  

Well, we Humans developed a Math using a base of 10 (because it's easy to use with decimals; and, you have 10 fingers and 10 toes ). However, nature uses the base we know as e (e = 2.72...)... However, ever tried counting in base e? It's a pain in the ***, to say the least...

Math exists in nature, just like the laws of Physics do. (In fact, Math is the language of Physics!) So, all the concepts of Math have been discovered (not invented) over the centuries, just like the concepts of Physics have been discovered (not invented) over the centuries.

It would be nice if we could invent Math though... but then that would mean we could change the laws of Physics too!