Basic question on numerical precision I appreciate this opportunity to submit a query on this forum.

When studying the continuous-time &amp; discrete-time distinction, specifically with reference to discrete signals being identical when separated by 2*pi, it has struck me that a basic premise, per google calc, doesn't hold:


exp(2 * pi * sqrt(-1)) = 1 
exp(4 * pi * sqrt(-1)) = 1 
exp(6 * pi * sqrt(-1)) = 1
exp(8 * pi * sqrt(-1)) = 1


but...


exp(10 * pi * sqrt(-1)) = 1 - 1.2246468 × 10^-15 i


Any thoughts on the above (discrepancy?) would be appreciated.

Regards,

wirefree
Writing another way

$$1 - 1.2246468 × 10^{-15} i = 1 - 0.0000000000000012246468i$$

It is just rounding errors adding up due to having a limited number of bits in whatever computer is doing the calculation.