You can't have two constructors (or any functions) with the same signatures. The best solution is probably to create classes for your coordinate types and overload on those. For example:
struct CartCoord {
CartCoord( double re, double img ) : mRe(re), mImg(img) {}
double mRe, mImg;
};
struct PolarCoord {
PolarCoord( double a, double v ) : mA(a), mV(v) {}
double mA, mV;
};
Then your constructors become:
Complex( const CartCoord & c );
Complex( const PolarCoord & c);
In use:
Complex c( CartCoord( 1, 2 ) );
You can also use them with overloaded operators of the Complex class. For example, assuming you have a binary + operator for the class define as:
Complex operator+( const Complex &, const Complex & );
then:
Complex a( CartCoord( 0, 0 ) );
Complex b = a + PolarCoord( 1, 1 );
As we have a conversion constructor from PolarCoord to Complex, this will be used in the + expression. This is more natural (IMHO) than calling static functions to create the temporary..
This is an example of Koenig's dictum (or at least a version of it) - whenever faced with a difficult problem, introduce a new level of classes to solve it.