code: def test_dup_count_complex_roots_7():
      R, x = ring("x", ZZ)
  
      # (z-I-1)*(z+I-1)*(z-I+1)*(z+I+1)
      f = x**4 + 4
      assert R.dup_count_complex_roots(f, a, b) == 4
      assert R.dup_count_complex_roots(f, c, d) == 1
  
      # (z-I-1)*(z+I-1)*(z-I+1)*(z+I+1)*(z-2)
      f = x**5 - 2 * x**4 + 4 * x - 8
      assert R.dup_count_complex_roots(f, a, b) == 4
      assert R.dup_count_complex_roots(f, c, d) == 1
  
      # (z-I-1)*(z+I-1)*(z-I+1)*(z+I+1)*(z**2-2)
      f = x**6 - 2 * x**4 + 4 * x**2 - 8
      assert R.dup_count_complex_roots(f, a, b) == 4
      assert R.dup_count_complex_roots(f, c, d) == 1
  
      # (z-I-1)*(z+I-1)*(z-I+1)*(z+I+1)*(z-1)
      f = x**5 - x**4 + 4 * x - 4
      assert R.dup_count_complex_roots(f, a, b) == 5
      assert R.dup_count_complex_roots(f, c, d) == 2
  
      # (z-I-1)*(z+I-1)*(z-I+1)*(z+I+1)*(z-1)*z
      f = x**6 - x**5 + 4 * x**2 - 4 * x
      assert R.dup_count_complex_roots(f, a, b) == 6
      assert R.dup_count_complex_roots(f, c, d) == 3
  
      # (z-I-1)*(z+I-1)*(z-I+1)*(z+I+1)*(z+1)
      f = x**5 + x**4 + 4 * x + 4
      assert R.dup_count_complex_roots(f, a, b) == 5
      assert R.dup_count_complex_roots(f, c, d) == 1
  
      # (z-I-1)*(z+I-1)*(z-I+1)*(z+I+1)*(z+1)*z
      f = x**6 + x**5 + 4 * x**2 + 4 * x
      assert R.dup_count_complex_roots(f, a, b) == 6
      assert R.dup_count_complex_roots(f, c, d) == 2
  
      # (z-I-1)*(z+I-1)*(z-I+1)*(z+I+1)*(z-1)*(z+1)
      f = x**6 - x**4 + 4 * x**2 - 4
      assert R.dup_count_complex_roots(f, a, b) == 6
      assert R.dup_count_complex_roots(f, c, d) == 2
  
      # (z-I-1)*(z+I-1)*(z-I+1)*(z+I+1)*(z-1)*(z+1)*z
      f = x**7 - x**5 + 4 * x**3 - 4 * x
      assert R.dup_count_complex_roots(f, a, b) == 7
      assert R.dup_count_complex_roots(f, c, d) == 3
  
      # (z-I-1)*(z+I-1)*(z-I+1)*(z+I+1)*(z-1)*(z+1)*(z-I)*(z+I)
      f = x**8 + 3 * x**4 - 4
      assert R.dup_count_complex_roots(f, a, b) == 8
      assert R.dup_count_complex_roots(f, c, d) == 3
  
imports: from sympy.polys.rings import ring
  from sympy.polys.domains import ZZ, QQ, ZZ_I, EX
  from sympy.polys.polyerrors import DomainError, RefinementFailed, PolynomialError
  from sympy.polys.rootisolation import dup_cauchy_upper_bound, dup_cauchy_lower_bound, dup_mignotte_sep_bound_squared
  from sympy.testing.pytest import raises
label_desc: Use image node_id 17 for calling a global function with example usage: test_dup_count_complex_roots_7() without return types