DLMF:4.45.E16 (Q2025)

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DLMF:4.45.E16
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    Statements

    Defining formula
    e z = e ℜ ⁡ z ⁢ ( cos ⁡ ( ℑ ⁡ z ) + i ⁢ sin ⁡ ( ℑ ⁡ z ) ) . superscript 𝑒 𝑧 superscript 𝑒 𝑧 𝑧 𝑖 𝑧 {\displaystyle{\displaystyle e^{z}=e^{\Re z}(\cos\left(\Im z\right)+i\sin\left% (\Im z\right)).}}
    0 references
    DLMF id
    DLMF:4.45.E16
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
     
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