DLMF:4.45.E16 (Q2025): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2aadec

Revision as of 19:27, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:4.45.E16
No description defined

    Statements

    e z = e z ( cos ( z ) + i sin ( 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:4.45.E16
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2aadec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2aadec
    0 references
    absent {\displaystyle{\displaystyle\Im}}
    C1.S9.E2.m2adec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aadec
    0 references