Constructor of base class in CRPT pattern

I'm using the CRPT pattern for a complex class (for learning).

I created a complex base class with a derived cartesian class, so I can add a complex<polar> class after. I have this piece of code working properly.

#include <iostream>

template<typename T>
class complex{
    public:
        using value_type = double;
        value_type re(){return static_cast<T*>(this)->re();}
};

class cartesian : public complex<cartesian>{
    public:
        using value_type = double;
        value_type re() const {return 1;}
    private:
        value_type re_;
};

int main(){
    complex<cartesian> c;
    std::cout << c.re();
}

It works, but when I want to add a constructor to initialize the re_ variable:

#include <iostream>

template<typename T>
class complex{
    public:
        using value_type = double;
        complex(){static_cast<T*>(this)->cartesian();}
        value_type re(){return static_cast<T*>(this)->re();}
};

class cartesian : public complex<cartesian>{
    public:
        using value_type = double;
        cartesian() : re_(2){}
        value_type re() const {return re_;}
    private:
        value_type re_;
};

int main(){
    complex<cartesian> c;
    std::cout << c.re();
}

I get this error:

main.cpp: In instantiation of ‘complex<T>::complex() [with T = cartesian]’:
main.cpp:15:28:   required from here
main.cpp:8:42: error: invalid use of ‘cartesian::cartesian’
    8 |         complex(){static_cast<T*>(this)->cartesian();}
      |                   ~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~

I guess the implementation for constructors is different? Any solution?