DLMF:4.14.E3 (Q1655)

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DLMF:4.14.E3
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    Statements

    Defining formula
    cos ⁡ z ± i ⁢ sin ⁡ z = e ± i ⁢ z , plus-or-minus 𝑧 𝑖 𝑧 superscript 𝑒 plus-or-minus 𝑖 𝑧 {\displaystyle{\displaystyle\cos z\pm i\sin z=e^{\pm iz},}}
    0 references
    DLMF id
    DLMF:4.14.E3
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    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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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.m2abdec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
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    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1bdec
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