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+--- Thread: Euler RE(e^(318310*i*pi)) ≠ 1 (/thread-20930.html)
Euler RE(e^(318310*i*pi)) ≠ 1 - Gil - 12-01-2023 12:24 PM
Euler
From integer n=0 to n=159154
RE(e^(2*n*i*pi)) = 1
And then, suddenly,
starting from n=159155:
RE(e^(318310*i*pi)) ≠ 1
RE(e^(318312*i*pi)) = 1
RE(e^(318314*i*pi)) ≠ 1
RE(e^(318316*i*pi)) = 1
RE(e^(318318*i*pi)) ≠ 1
RE(e^(318320*i*pi)) = 1
...
the above unexpected series of results seem to repeat itself forever.
Somewhat ennoying.
Of course we should simplify such expressions with n big.
Nethertheless...
Besides all
IM(e^(2*n*i*pi)), with n=integer≠0, never gives 0.
Could that issues be fixed up?
Note that these very same "behaviours" were already to be met with the HP50G.
RE: Euler RE(e^(318310*i*pi)) ≠ 1 - parisse - 12-01-2023 07:55 PM
I just checked with my devel version, it works in CAS. In home, since computations are done in approx. mode, you can not expect exact value for exp(2*i*n*pi) for n integer.