DLMF:4.45.E15 (Q2024)

From testwiki
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:4.45.E15
No description defined

    Statements

    test
    ln ⁡ z = ln ⁡ | z | + i ⁢ ph ⁡ z , 𝑧 𝑧 𝑖 phase 𝑧 {\displaystyle{\displaystyle\ln z=\ln|z|+i\operatorname{ph}z,}}
    0 references
    DLMF id
    DLMF:4.45.E15
    0 references
    constraint
    - π ≤ ph ⁡ z ≤ π 𝜋 phase 𝑧 𝜋 {\displaystyle{\displaystyle-\pi\leq\operatorname{ph}z\leq\pi}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    Q11217
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1dec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q2024&oldid=9696"