I can put Euler's Equation into words, but not into descriptive words which make the operations clear. What does it mean, for instance, to raise a number to a complex power? I love how this equation describes all of math, contains all the fundamental numbers, and relates the operands to the underlying geometry around the origin and the complex plane. I just wish I had a natural language way to express what it says.
+9664 \(a^i = {a}^{{-1}^{1/2}} = {a}^{{1/2}^{-1}}=\frac{1}{\sqrt{a}}?\)
That's only what i thinks
It may NOT be real
+9664 The exponential function e^z can be defined as the limit of (1 + z/N)N, as Napproaches infinity, and thus eiπ is the limit of (1 +iπ/N)N. The computation of (1 + iπ/N)N is displayed as the combined effect of N repeated multiplications in the complex plane, with the final point being the actual value of (1 +iπ/N)N. It can be seen that as N gets larger (1 +iπ/N)Napproaches a limit of −1.
Source: Wikipedia.
I think that means the y axis represents complex numbers i , 2i , 3i ...... and x axis represents real numbers 1, 2, 3 .....
