| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
-� 1 1 1 i -i
-� = ----- = --------- = --------- = --------- = ---------
� sqr(-�) sqr(�)i -sqr(�) sqr(�)
-�
-i -i -2i
= ---------- = ---------- = -------- = -sqr(2)i
1 sqr(2) sqr(2)
-------- --------
sqr(2) 2
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1069.1 | did you format that all by hand? | AITG::DERAMO | Daniel V. {AITG,ZFC}:: D'Eramo | Fri Apr 28 1989 17:14 | 19 |
He's right. And in the next version of VAX LISP, Lisp> (setq q1 (expt -0.5l0 -0.5l0)) #C(6.13189574817272264384187434308639L-35 -1.4142135623730950488016887242096L0) which is about as close to Lisp> (setq q2 (* (- (sqrt 2.0l0)) (complex 0.0l0 1.0l0))) #C(0.0L0 -1.4142135623730950488016887242096L0) as you can get. Lisp> (- q1 q2) #C(6.13189574817272264384187434308639L-35 0.0L0) i So what is i (neat: the principal value is real!)? Dan | |||||
| 1069.4 | i^i= | SDOGUS::HOOKER | Waikiki when you can San Diego | Mon May 01 1989 11:59 | 11 |
i^i = exp(-pi/2)!!!!
Proof:
i=cos(pi/2) + i*sin(pi/2) (DeMouve's theorem)
=exp(i*pi/2)
i^i = exp (i*(i*pi/2)) = exp (-1*pi/2) = exp(-pi/2)
Hooker
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| 1069.5 | AITG::DERAMO | Daniel V. {AITG,ZFC}:: D'Eramo | Mon May 01 1989 14:30 | 7 | |
re .-1
Yes. By the way, all of the values (obtained from
log i = i pi/2 + 2 pi i k for k = ..., -2, -1, 0, 1, 2, ...)
are real. Seems strange, doesn't it?
Dan
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