DLMF:4.45.E16 (Q2025)

No description defined

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

Statements

Defining formula

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{z}=e^{\realpart@@{z}}(\cos@{\imagpart@@{z}}+i\sin@{\imagpart@@{z}}).}

0 references

DLMF id

DLMF:4.45.E16

0 references

Symbols used

cosine function

Defining formula

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\NVar{z}}}

xml-id

C4.S14.E2.m2aadec

0 references

base of natural logarithm

Defining formula

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}

xml-id

C4.S2.E11.m2aadec

0 references

Q10901

Defining formula

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \imagpart@@}

xml-id

C1.S9.E2.m2adec

0 references

imaginary unit

Defining formula

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}

xml-id

C1.S9.E1.m2aadec

0 references

Q10811

Defining formula

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@}

xml-id

C1.S9.E2.m1adec

0 references

sine function

Defining formula

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\NVar{z}}}

xml-id

C4.S14.E1.m2aadec

0 references

Q11217

Defining formula

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}

xml-id

C4.S1.XMD8.m1adec

0 references