2010-11-03, 02:31 AM
Imagine and numbers as vectors on a complex plane (x-axis is real and y-axis is imaginary).
![[Image: complex_plane.gif]](http://1.bp.blogspot.com/_0tb8Gps8nZU/SxKMgQBrVeI/AAAAAAAAAA8/zTIvcWgmutM/s320/complex_plane.gif)
Usually when you multiply a real number with (-1), the direction simply flips once (a 180 degree turn or pi radian) and flips twice when you multiply (-1) twice (a 360 degree turn or 2 pi radian). Since you're spinning it pi times, you simply rotate the vector 180*pi degrees or pi² radian. You then use trig to find out where the vector ends which yields
It's probably easier to visualize the problem and tackle it geometrically than to think about it arithmetically.
Usually when you multiply a real number with (-1), the direction simply flips once (a 180 degree turn or pi radian) and flips twice when you multiply (-1) twice (a 360 degree turn or 2 pi radian). Since you're spinning it pi times, you simply rotate the vector 180*pi degrees or pi² radian. You then use trig to find out where the vector ends which yields
Shidoshi Wrote:cos(pi²+ i*sin(pi²
It's probably easier to visualize the problem and tackle it geometrically than to think about it arithmetically.