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Topic: on real part of [(1+isqrt(7))/2]^n
Replies: 20   Last Post: Feb 15, 2014 5:52 AM

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 Robin Chapman Posts: 412 Registered: 5/29/08
Re: on real part of [(1+isqrt(7))/2]^n
Posted: Feb 11, 2014 11:23 AM

On 11/02/2014 16:12, konyberg wrote:

> a_n = Re(a^n)
> a^n = (x + iy)^n = r^n (cos(nu) + isin(nu))
> a_n = r^n cos(nu)
> a = (1 + isqrt(7))/2 gives r = sqrt(2), and u = pi/4 (45 deg)

Oh no, u = tan^{-1}(sqrt(7)) which is not a rational multiple of pi.

Date Subject Author
2/10/14 AP
2/10/14 Brian Q. Hutchings
2/10/14 Pubkeybreaker
2/10/14 Karl-Olav Nyberg
2/10/14 William Elliot
2/11/14 AP
2/11/14 Karl-Olav Nyberg
2/11/14 Robin Chapman
2/11/14 Karl-Olav Nyberg
2/11/14 Robin Chapman
2/11/14 Karl-Olav Nyberg
2/11/14 Karl-Olav Nyberg
2/15/14 Karl-Olav Nyberg
2/15/14 quasi
2/15/14 Karl-Olav Nyberg
2/15/14 quasi
2/11/14 William Elliot
2/11/14 Robin Chapman
2/11/14 William Elliot
2/13/14 quasi
2/14/14 Brian Q. Hutchings