(In reply to
what I find by Charlie)
I don't have an analytic solution, but there there's a bit that can teased out of your findings. Some of those 'complex' solutions have imaginary parts that are suspiciously small.
Take the 7th one on the list: -2.61799387799149 + 5.55111512312578e-17i
Maybe this is just -5pi/6
sin(-5pi/6)=-1/2
cos(-5pi/6)=-sqrt(3)/2
sin(-5pi/6)^10+cos(-5pi/6)^10=1/1024+243/1024=244/1024=61/256
So, they are just real solutions with period pi/2:
pi/6+n*pi/2, pi/3+n*pi/2,
You can also see the real parts of many pairs that are indeed complex sum to pi.
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Posted by Jer
on 2023-07-12 16:15:33 |
re: what I find Overlooked
