WP 34S and 31S bugs and fixes

05232017, 12:19 PM
(This post was last modified: 05232017 12:24 PM by Dieter.)
Post: #281




RE: WP 34S and 31S bugs and fixes
(05232017 12:00 PM)Briancady413 Wrote: I calculated e^(i*Pi) and got a real component of 1(as should be) plus a tiny imaginary component, which I believe shouldn't be there. This is not a bug, it is the correct result. Remember: pi is an irrational number with infinitely many digits. But your calculator uses only 16 resp. 34 digits, so you cannot enter pi, you can only enter a close approximation. The first 16 (or 34) digits are all you can provide. So you do not calculate e^(i*pi) but e^(i*3,141592653589793). The imaginary part of this is approx. pi – 3,141592653589793 so that you get i * 2,3846...E–16. Or switch to double precision and get i * –1,158...E–34. The same happens if you try to calculate sin(pi). You won't get zero but again a very tiny residual. That's again because you do not calculate sin(pi) but sin(3,141592653589793) which is 2,3846 E–16. Dieter 

05232017, 01:18 PM
(This post was last modified: 05232017 01:19 PM by toml_12953.)
Post: #282




RE: WP 34S and 31S bugs and fixes  
05232017, 05:05 PM
(This post was last modified: 05232017 09:31 PM by Dieter.)
Post: #283




RE: WP 34S and 31S bugs and fixes
(05232017 01:18 PM)toml_12953 Wrote: If it's any consolation, the HP Prime gets This should be the result from any 12digit calculator (the 35s returns the same). The imaginary part of e^(i*pi) is sin(pi), resp. here sin(3,1415926...), which is approximately pi – 3,1415926... . The 12digit machines use "pi"=3,14159265359, so the imaginary part here is ~ pi – 3,14159265359 = –2,06761537357 E–13. In the same way a 10digit calculator should return pi – 3,141592654 = –4,102067615 E–10. But since most of these calculators internally use 13 digits for pi I'd expect not more than –4,10 E–10. Dieter Edit: corrected the value for 10digit devices 

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