tag:blogger.com,1999:blog-3500036.post1292993751447433700..comments2024-01-02T04:49:16.658-05:00Comments on He Lives: Math PuzzleDavidhttp://www.blogger.com/profile/08688240424047203541noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-3500036.post-81636377098928649532017-11-28T11:57:14.857-05:002017-11-28T11:57:14.857-05:00Ahh... I've been found out!Ahh... I've been found out! Davidhttps://www.blogger.com/profile/08688240424047203541noreply@blogger.comtag:blogger.com,1999:blog-3500036.post-70943945781380280752017-11-28T11:47:44.400-05:002017-11-28T11:47:44.400-05:00One raised to any power is not "still just on...One raised to any power is not "still just one".<br />For fractional powers (p), things get tricky. For example, 1^(1/2) (i.e., the square root of 1), could be 1, or it could be -1. Similarly, 1^(1/4) could be i, or -i, or 1 or -1.<br />The formula cos(2\pip) + i sin(2\pip) gives one of these solutions in both of these cases [i.e., cos(\pi) + i sin(\pi) = -1 and cos(\pi/2) + i sin(\pi/2) = i] and provides a solution in the case of p=\piDoughttps://www.blogger.com/profile/16197663817396506388noreply@blogger.com