DLMF:4.4.E6 (Q1540)

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DLMF:4.4.E6
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    Statements

    Defining formula
    e ± π ⁢ i / 2 = ± i , superscript 𝑒 plus-or-minus 𝜋 imaginary-unit 2 plus-or-minus imaginary-unit {\displaystyle{\displaystyle e^{\pm\pi\mathrm{i}/2}=\pm\mathrm{i},}}
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    DLMF id
    DLMF:4.4.E6
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
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