Unraveling Euler's Formula: e^(pi*i) +1 = 0

[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...?

 

[HallsofIvy]

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

(click on that to see the code I used)

I suspect that just about everyone on this board already knows that- there have been a number of threads about it.

 

[strid]

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

 

[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...