DLMF:4.2.E23 (Q1562)

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DLMF:4.2.E23
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    Statements

    DLMF defining formula
    ph ⁡ ( exp ⁡ z ) = ℑ ⁡ z + 2 ⁢ k ⁢ π , phase 𝑧 𝑧 2 𝑘 𝜋 {\displaystyle{\displaystyle\operatorname{ph}\left(\exp z\right)=\Im z+2k\pi,}}
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    constraint
    k ∈ ℤ 𝑘 {\displaystyle{\displaystyle k\in\mathbb{Z}}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
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    Q10758
    DLMF defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
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    exponential function
    DLMF defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2addec
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    imaginary part
    DLMF defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2adec
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    Q10792
    DLMF defining formula
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2adec
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    phase
    DLMF defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1abdec
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    integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C4.S1.XMD1.m1adec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1pdec
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    Identifiers

     
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