Playing around with some numbers may help:

from math import remainder, fmod

# in case x is a multiple of y
remainder(20, 4)    # 0.0
fmod(20, 4)         # 0.0

# in any other case
remainder(20, 3)    # -1.0
fmod(20, 3)         # 2.0

So what we see here is that the remainder, as stated in the docs, returns the difference between x and the closest integer multiple of y. As 20 lies between 18 and 21 (the 6- and 7-multiples of 3), it chooses whichever is closer to x. In this case it is 21, so the difference between x and 21 is -1.0.

In contrast, fmod returns the result of 20 mod 3, which is 2.0. I explicitly do not use the % operator, as the docs state that the result may differ.

The % operator and math.fmod do not perform the same modulo operation. In specific, the handling of negative numbers is different:

math.fmod(x, y)

[..] The intent of the C standard is that fmod(x, y) be exactly (mathematically; to infinite precision) equal to x - n*y for some integer n such that the result has the same sign as x and magnitude less than abs(y). Python’s x % y returns a result with the sign of y instead, and may not be exactly computable for float arguments. [..]

Binary arithmetic operations

[..] The modulo operator always yields a result with the same sign as its second operand (or zero); [..] The function math.fmod() returns a result whose sign matches the sign of the first argument instead [..]. Which approach is more appropriate depends on the application.

>>> def test_mod(a, b): print('%-op:', a % b, 'fmod:', fmod(a, b))
>>> test_mod(10, 12)
%-op: 10 fmod: 10.0
>>> test_mod(-10, 12)
%-op: 2 fmod: -10.0
>>> test_mod(10, -12)
%-op: -2 fmod: 10.0

Both ans variants will give the same result for positive inputs:

>>> perc_ans([6, 3, 10, 0, 2], 5)
180
>>> math_ans([6, 3, 10, 0, 2], 5)
180
>>> perc_ans([6, -3, -10, 0, 2], 5)
999999989
>>> math_ans([6, -3, -10, 0, 2], 5)
180

The result you got was a complex number because you exponentiated a negative number. i and j are just notational choices to represent the imaginary number unit, i being used in mathematics more and j being used in engineering more. You can see in the docs that Python has chosen to use j:

https://docs.python.org/2/library/cmath.html#conversions-to-and-from-polar-coordinates