# Why gives Modulo of complex numbers different answers for rationals and reals

When running

Table[1.*Mod[(1 + I)^(1 + k*I), 1 + k*I], {k, 49, 50, 0.5}]
Table[1.*Mod[(1 + I)^(1 + k*I), 1 + k*I], {k, 49, 50, 1/2}]


I get for the first table

{1.28398*10^-17 - 2.4145*10^-17 I, 1.1351*10^-17 - 1.45645*10^-17 I,
9.24544*10^-18 - 8.36557*10^-18 I}


and for the second table completely different values:

{-48. + 50. I, -48.5 + 50.5 I, -49. + 51. I}


In Mathematica 12.0.0.0. Any explanation?

• Mod for approximate moduli just gives a result that lies within a disk of the minimal radius based on the modulus. With exact moduli there is a different normalization convention based on Quotient; see the Details and Options section on the reference page. – Daniel Lichtblau Apr 22 at 22:04
• What Option settings are you referring to? – user57467 Apr 23 at 0:55
• I made no claim about Option settings. Indeed, Mod takes no options. – Daniel Lichtblau Apr 23 at 15:27