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+--- Thread: A math dilemma (/showthread.php?tid=32216)
A math dilemma - Shidoshi - 2010-11-02
How do you calculate the value for (-1)^pi?
Or rather, how do you calculate (-1)^a, where "a" is irrational.
A math dilemma - Corn - 2010-11-02
Well, according to my calculator, it is -0.9026853619-0.430301216i, so yeah. Not exactly sure how to calculate it, sorry =/.
A math dilemma - Five Second Pose - 2010-11-02
I don't know the exact method, but I know it involves using logs to change the base of -1 to make it one number to the power of an integer.
A math dilemma - Shidoshi - 2010-11-02
Hmm just searched wolfram-alpha.
you just use these identities:
e^(i*pi) = -1
e^(i*x) = cos(x) + i*sin(x)
so (-1)^pi = e^(i*pi)^pi = e^(i*pi²
= cos(pi² + i*sin(pi²so it's the value posted by Corn, yeah.
A math dilemma - Cyadd - 2010-11-02
[COLOR="Red"]Wolfram states it's equal to -1.
Edit: beat me to it.
[/COLOR]
A math dilemma - larmie - 2010-11-03
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
Shidoshi Wrote:cos(pi²
It's probably easier to visualize the problem and tackle it geometrically than to think about it arithmetically.