DLMF:1.9.E22 (Q296)

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DLMF:1.9.E22
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    Statements

    Defining formula
    cos ⁡ n ⁢ θ + i ⁢ sin ⁡ n ⁢ θ = ( cos ⁡ θ + i ⁢ sin ⁡ θ ) n , 𝑛 𝜃 𝑖 𝑛 𝜃 superscript 𝜃 𝑖 𝜃 𝑛 {\displaystyle{\displaystyle\cos n\theta+i\sin n\theta=(\cos\theta+i\sin\theta% )^{n},}}
    0 references
    DLMF id
    DLMF:1.9.E22
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    constraint
    n ∈ ℤ 𝑛 {\displaystyle{\displaystyle n\in\mathbb{Z}}}
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    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
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    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2acdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
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    Q10818
    Defining formula
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2aadec
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