Well, not really a complex parser, but a parser that parses complex numbers.

Here's a simple parser expression for complex numbers:

    '(' >> double_ >> -(',' >> double_) >> ')'
|   double_

What's new? Well, we have:

The complex parser presented above reads as:

This parser can parse complex numbers of the form:

(123.45, 987.65)
(123.45)
123.45

Here goes, this time with actions:

namespace client
{
    template <typename Iterator>
    bool parse_complex(Iterator first, Iterator last, std::complex<double>& c)
    {
        using boost::spirit::x3::double_;
        using boost::spirit::x3::_attr;
        using boost::spirit::x3::phrase_parse;
        using boost::spirit::x3::ascii::space;

        double rN = 0.0;
        double iN = 0.0;
        auto fr = [&](auto& ctx){ rN = _attr(ctx); };
        auto fi = [&](auto& ctx){ iN = _attr(ctx); };

        bool r = phrase_parse(first, last,

            //  Begin grammar
            (
                    '(' >> double_[fr]
                        >> -(',' >> double_[fi]) >> ')'
                |   double_[fr]
            ),
            //  End grammar

            space);

        if (!r || first != last) // fail if we did not get a full match
            return false;
        c = std::complex<double>(rN, iN);
        return r;
    }
}

The full cpp file for this example can be found here: complex_number.cpp

The double_ parser attaches this action:

[&](auto& ctx){ n = _attr(ctx); }

This assigns the parsed result (actually, the attribute of double_) to n.