There is a sympy issue (we could check if we create an issue there) concerning "zero", what is zero?
x, y, c, d = symbols('x, y, c, d', real = True)
f=(7.6I(x + Iy) - 15.3215831575369I)/(-2.01599778388644x - 2.01599778388644I*y + 1)
gives
simplify(diff(im(f), y)-diff(re(f), x)) equal to somethin of the order 10**(-16)
simplify(diff(im(f), x)+diff(re(f), y)) equal to somethin of the order 10**(-16)
while
f=(7.6I(x + Iy) - cI)/(-dx - dI*y + 1)
print()
print(simplify(diff(im(f), x)+diff(re(f), y)))
print()
print(simplify(diff(im(f), y)-diff(re(f), x)))
print()
gives zero...
check_anyltic_sympy_issue.zip