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A309949
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Decimal expansion of the imaginary part of the square root of 1 + i.
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3
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4, 5, 5, 0, 8, 9, 8, 6, 0, 5, 6, 2, 2, 2, 7, 3, 4, 1, 3, 0, 4, 3, 5, 7, 7, 5, 7, 8, 2, 2, 4, 6, 8, 5, 6, 9, 6, 2, 0, 1, 9, 0, 3, 7, 8, 4, 8, 3, 1, 5, 0, 0, 9, 2, 5, 8, 8, 2, 5, 9, 5, 6, 9, 4, 9, 0, 8, 0, 0, 2, 0, 3, 2, 3, 3, 4, 4, 8, 2, 9, 1, 5, 9, 1, 4, 0, 1, 8, 1, 9, 7, 6, 1, 0, 2
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OFFSET
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0,1
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COMMENTS
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i is the imaginary unit such that i^2 = -1.
Multiplied by -1, this is the imaginary part of the square root of 1 - i. And also the real part of -sqrt(1 + i) - i + sqrt(1 + i)^3, which is a unit in Q(sqrt(1 + i)).
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LINKS
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FORMULA
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Equals sqrt(1/sqrt(2) - 1/2) = 2^(1/4) * sin(Pi/8).
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EXAMPLE
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Im(sqrt(1 + i)) = 0.45508986056222734130435775782247...
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MAPLE
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Digits := 120: Re(sqrt(-1 - I))*10^95:
ListTools:-Reverse(convert(floor(%), base, 10)); # Peter Luschny, Sep 20 2019
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MATHEMATICA
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RealDigits[Sqrt[1/Sqrt[2] - 1/2], 10, 100][[1]]
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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