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A309948 Decimal expansion of the real part of the square root of 1 + i. 3

%I

%S 1,0,9,8,6,8,4,1,1,3,4,6,7,8,0,9,9,6,6,0,3,9,8,0,1,1,9,5,2,4,0,6,7,8,

%T 3,7,8,5,4,4,3,9,3,1,2,0,9,2,7,1,5,7,7,4,3,7,4,4,4,1,1,5,7,8,8,4,2,8,

%U 7,5,0,5,3,5,5,5,2,8,4,8,1,1,1,3,6,5,3,6,0,6,6,3,5,6,4,1

%N Decimal expansion of the real part of the square root of 1 + i.

%C i is the imaginary unit such that i^2 = -1.

%C Also imaginary part of sqrt(-1 + i).

%F Re(sqrt(1 + i)) = sqrt(1/2 + 1/sqrt(2)) = 2^(1/4) * cos(Pi/8).

%F Equals Im(-sqrt(-1 - i)). - _Peter Luschny_, Sep 20 2019

%e Re(sqrt(1 + i)) = 1.09868411346780996603980119524...

%p Digits := 120: Im(-sqrt(-1 - I))*10^95:

%p ListTools:-Reverse(convert(floor(%), base, 10)); # _Peter Luschny_, Sep 20 2019

%t RealDigits[Sqrt[1/2 + 1/Sqrt[2]], 10, 100][[1]]

%o (PARI) real(sqrt(1+I)) \\ _Michel Marcus_, Sep 16 2019

%Y Cf. A309949 (imaginary part).

%K nonn,cons,easy

%O 1,3

%A _Alonso del Arte_, Aug 24 2019

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Last modified September 27 19:34 EDT 2021. Contains 347694 sequences. (Running on oeis4.)