Iota raise to the power iota
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cos@ + i.sin@ = e^(i.@)
if we take @ = pi/2:
i = e^(i.pi*/2)
Raise both sides to exponent i:
i^i = e^ (i.pi/2 . i)
i^i = e^(-pi/2)
if we take @ = pi/2:
i = e^(i.pi*/2)
Raise both sides to exponent i:
i^i = e^ (i.pi/2 . i)
i^i = e^(-pi/2)
Rajvardhan25:
I want from Euler identity
First thing all the answers here are wrong,
Exponents are associative from right i.e.
iii=i(ii)≠(ii)iiii=i(ii)≠(ii)i
Lets calculate iiii first,
x=iix=ii
xi=i−1=−i=e−iπ/2xi=i−1=−i=e−iπ/2
x=e−π/2x=e−π/2
iii=z=ix=iexp(−π/2)iii=z=ix=iexp(−π/2)
=(exp(iπ/2))exp(−π/2)=(exp(iπ/2))exp(−π/2)
=exp(i(π2exp(−π2)))=exp(i(π2exp(−π2)))
Let y=π2exp(−π2)≈0.3265364749...y=π2exp(−π2)≈0.3265364749...
z=eiy=cos(y)+isin(y)z=eiy=cos(y)+isin(y)
z≈0.947159+0.32076445iz≈0.947159+0.32076445i
i^(i^i) =
0.947158998 + 0.94715899807
Exponents are associative from right i.e.
iii=i(ii)≠(ii)iiii=i(ii)≠(ii)i
Lets calculate iiii first,
x=iix=ii
xi=i−1=−i=e−iπ/2xi=i−1=−i=e−iπ/2
x=e−π/2x=e−π/2
iii=z=ix=iexp(−π/2)iii=z=ix=iexp(−π/2)
=(exp(iπ/2))exp(−π/2)=(exp(iπ/2))exp(−π/2)
=exp(i(π2exp(−π2)))=exp(i(π2exp(−π2)))
Let y=π2exp(−π2)≈0.3265364749...y=π2exp(−π2)≈0.3265364749...
z=eiy=cos(y)+isin(y)z=eiy=cos(y)+isin(y)
z≈0.947159+0.32076445iz≈0.947159+0.32076445i
i^(i^i) =
0.947158998 + 0.94715899807
Answered by
0
cos@ + i.sin@ = e^(i.@)
if we take @ = pi/2:
i = e^(i.pi*/2)
Raise both sides to exponent i:
i^i = e^ (i.pi/2 . i)
i^i = e^(-pi/2)
if we take @ = pi/2:
i = e^(i.pi*/2)
Raise both sides to exponent i:
i^i = e^ (i.pi/2 . i)
i^i = e^(-pi/2)
Exponents are associative from right i.e.
iii=i(ii)≠(ii)iiii=i(ii)≠(ii)i
Lets calculate iiii first,
x=iix=ii
xi=i−1=−i=e−iπ/2xi=i−1=−i=e−iπ/2
x=e−π/2x=e−π/2
iii=z=ix=iexp(−π/2)iii=z=ix=iexp(−π/2)
=(exp(iπ/2))exp(−π/2)=(exp(iπ/2))exp(−π/2)
=exp(i(π2exp(−π2)))=exp(i(π2exp(−π2)))
Let y=π2exp(−π2)≈0.3265364749...y=π2exp(−π2)≈0.3265364749...
z=eiy=cos(y)+isin(y)z=eiy=cos(y)+isin(y)
z≈0.947159+0.32076445iz≈0.947159+0.32076445i
i^(i^i) =
0.947158998 + 0.94715899807
iii=i(ii)≠(ii)iiii=i(ii)≠(ii)i
Lets calculate iiii first,
x=iix=ii
xi=i−1=−i=e−iπ/2xi=i−1=−i=e−iπ/2
x=e−π/2x=e−π/2
iii=z=ix=iexp(−π/2)iii=z=ix=iexp(−π/2)
=(exp(iπ/2))exp(−π/2)=(exp(iπ/2))exp(−π/2)
=exp(i(π2exp(−π2)))=exp(i(π2exp(−π2)))
Let y=π2exp(−π2)≈0.3265364749...y=π2exp(−π2)≈0.3265364749...
z=eiy=cos(y)+isin(y)z=eiy=cos(y)+isin(y)
z≈0.947159+0.32076445iz≈0.947159+0.32076445i
i^(i^i) =
0.947158998 + 0.94715899807
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