DLMF:1.9.E10 (Q284)

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DLMF:1.9.E10
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    Statements

    Defining formula
    e i ⁢ θ = cos ⁡ θ + i ⁢ sin ⁡ θ ; superscript 𝑒 𝑖 𝜃 𝜃 𝑖 𝜃 {\displaystyle{\displaystyle e^{i\theta}=\cos\theta+i\sin\theta;}}
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    DLMF id
    DLMF:1.9.E10
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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.m2aadec
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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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