DLMF:10.17.E7 (Q3176)

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DLMF:10.17.E7
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    Statements

    Defining formula
    z 1 2 = exp ⁡ ( 1 2 ⁢ ln ⁡ | z | + 1 2 ⁢ i ⁢ ph ⁡ z ) . superscript 𝑧 1 2 1 2 𝑧 1 2 𝑖 phase 𝑧 {\displaystyle{\displaystyle z^{\frac{1}{2}}=\exp\left(\tfrac{1}{2}\ln|z|+% \tfrac{1}{2}i\operatorname{ph}z\right).}}
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    DLMF id
    DLMF:10.17.E7
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    Symbols used
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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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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