Add example for degree_complex/halfdegree to docstring

src/complex.jl

@@ -245,6 +245,10 @@ end
 Return the _total complex degree_ of the monomial of the term `t`, i.e., the maximum of the total degree of the declared
 variables in `t` and the total degree of the conjugate variables in `t`.
 To be well-defined, the monomial must not contain real parts or imaginary parts of variables.
+If `x` is a real-valued variable and `z` is complex-valued,
+- `degree_complex(x^5) = 5`
+- `degree_complex(z^3 * conj(z)^4) = 4` and `degree_complex(z^4 * conj(z)^3) = 4`
+- `degree_complex(x^5 * z^3 * conj(z^4)) = 5 + 4 = 9`
 """
 degree_complex(t::AbstractTermLike)
 
@@ -253,6 +257,11 @@ degree_complex(t::AbstractTermLike)
 
 Return the equivalent of `ceil(degree(t)/2)`` for real-valued terms or `degree_complex(t)` for terms with only complex
 variables; however, respect any mixing between complex and real-valued variables.
+To be well-defined, the monomial must not contain real parts or imaginary parts of variables.
+If `x` is a real-valued variable and `z` is complex-valued,
+- `halfdegree(x^5) = 3`
+- `halfdegree(z^3 * conj(z)^4) = 4` and `halfdegree(z^4 * conj(z)^3) = 4`
+- `halfdegree(x^5 * z^3 * conj(z^4)) = 3 + 4 = 7`
 """
 halfdegree(t::AbstractTermLike)