# Cool thing

1. Mar 11, 2005

### strid

Just wanted to share a cool thing I found when I was shown Eulers formula...

e^(pi*i) +1 = 0

this can be written as

e^pi = (SQRT -1)ROOT -1

dont know if I wrote correclty...

...........................................................................................
...........................................................................................
..........$#....$$.......................... .$....#.......#.........#......................................................................
....#.#...--.#........#...................#...............................................
.....#..........#...... #....................#...............................................
........................#..........----...#...................................................
.......#.......................#......................................................
.................#...#........................#...............................................
..................#.#.........................#..............................................
...................#........................................................................
...........................................................................................

Took a time to write this :)

so can you imagine the number above to equal e^pi which is th real number around 23...? :rofl:

2. Mar 11, 2005

### HallsofIvy

Yes,
$$e^{i\pi}+ 1= 0$$

(click on that to see the code I used)

3. Mar 11, 2005

### strid

but is the format i wrote it in also well-known? the cool root stuff I mean...

4. Mar 11, 2005

### shmoe

Yes it is. Exponentiation by complex numbers gives some startling results when you first see it.

Note that $$e^{\pi}$$ isn't the only answer for $$(-1)^{1/i}$$, it depends on the branch of the logarithm you used. Can you find the other values? They might be even more suprising...