Why is $cos(i)-i sin(i)=e$? [duplicate]
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This question already has an answer here:
Why Euler's formula is true? [duplicate]
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When I was typing $cos(i)-i sin(i)$ into the calculator, I found out that it is equal to e (Euler's Constant). I was amazed by that "discovery" so I checked in on the internet and there was no results. Someone please explain the connection of imaginary numbers and Euler's Constant.
complex-numbers eulers-constant
edited Dec 13 '18 at 8:38
Martin Sleziak
44.7k10119272
asked Dec 12 '18 at 12:25
Mr. MathsMr. Maths
64
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marked as duplicate by lab bhattacharjee, Brahadeesh, Leucippus, Shailesh, Cesareo Dec 13 '18 at 8:52
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
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$begingroup$
This question already has an answer here:
Why Euler's formula is true? [duplicate]
1 answer
When I was typing $cos(i)-i sin(i)$ into the calculator, I found out that it is equal to e (Euler's Constant). I was amazed by that "discovery" so I checked in on the internet and there was no results. Someone please explain the connection of imaginary numbers and Euler's Constant.
complex-numbers eulers-constant
edited Dec 13 '18 at 8:38
Martin Sleziak
44.7k10119272
asked Dec 12 '18 at 12:25
Mr. MathsMr. Maths
64
$endgroup$
marked as duplicate by lab bhattacharjee, Brahadeesh, Leucippus, Shailesh, Cesareo Dec 13 '18 at 8:52
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
Why Euler's formula is true? [duplicate]
1 answer
When I was typing $cos(i)-i sin(i)$ into the calculator, I found out that it is equal to e (Euler's Constant). I was amazed by that "discovery" so I checked in on the internet and there was no results. Someone please explain the connection of imaginary numbers and Euler's Constant.
complex-numbers eulers-constant
edited Dec 13 '18 at 8:38
Martin Sleziak
44.7k10119272
asked Dec 12 '18 at 12:25
Mr. MathsMr. Maths
64
$endgroup$
This question already has an answer here:
Why Euler's formula is true? [duplicate]
1 answer
When I was typing $cos(i)-i sin(i)$ into the calculator, I found out that it is equal to e (Euler's Constant). I was amazed by that "discovery" so I checked in on the internet and there was no results. Someone please explain the connection of imaginary numbers and Euler's Constant.
This question already has an answer here:
Why Euler's formula is true? [duplicate]
1 answer
complex-numbers eulers-constant
complex-numbers eulers-constant
edited Dec 13 '18 at 8:38
Martin Sleziak
44.7k10119272
asked Dec 12 '18 at 12:25
Mr. MathsMr. Maths
64
edited Dec 13 '18 at 8:38
Martin Sleziak
44.7k10119272
asked Dec 12 '18 at 12:25
Mr. MathsMr. Maths
64
edited Dec 13 '18 at 8:38
Martin Sleziak
44.7k10119272
edited Dec 13 '18 at 8:38
Martin Sleziak
44.7k10119272
edited Dec 13 '18 at 8:38
Martin Sleziak
44.7k10119272
44.7k10119272
asked Dec 12 '18 at 12:25
Mr. MathsMr. Maths
64
asked Dec 12 '18 at 12:25
Mr. MathsMr. Maths
64
asked Dec 12 '18 at 12:25
Mr. MathsMr. Maths
64
64
marked as duplicate by lab bhattacharjee, Brahadeesh, Leucippus, Shailesh, Cesareo Dec 13 '18 at 8:52
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by lab bhattacharjee, Brahadeesh, Leucippus, Shailesh, Cesareo Dec 13 '18 at 8:52
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
add a comment |
1 Answer
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We have $e^{iz}=cos z+i sin z$ for all $z in mathbb C$. This can easily seen with power series. Now plug in $z=-i$.
answered Dec 12 '18 at 12:28
FredFred
46.9k1848
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
We have $e^{iz}=cos z+i sin z$ for all $z in mathbb C$. This can easily seen with power series. Now plug in $z=-i$.
answered Dec 12 '18 at 12:28
FredFred
46.9k1848
$endgroup$
add a comment |
$begingroup$
We have $e^{iz}=cos z+i sin z$ for all $z in mathbb C$. This can easily seen with power series. Now plug in $z=-i$.
answered Dec 12 '18 at 12:28
FredFred
46.9k1848
$endgroup$
add a comment |
$begingroup$
We have $e^{iz}=cos z+i sin z$ for all $z in mathbb C$. This can easily seen with power series. Now plug in $z=-i$.
answered Dec 12 '18 at 12:28
FredFred
46.9k1848
$endgroup$
We have $e^{iz}=cos z+i sin z$ for all $z in mathbb C$. This can easily seen with power series. Now plug in $z=-i$.
answered Dec 12 '18 at 12:28
FredFred
46.9k1848
answered Dec 12 '18 at 12:28
FredFred
46.9k1848
answered Dec 12 '18 at 12:28
FredFred
46.9k1848
answered Dec 12 '18 at 12:28
FredFred
46.9k1848
46.9k1848
add a comment |
add a comment |
