14.6 Mixed-Mode Arithmetic

Type complex is designed to fit in with the built-in arithmetic types in mixed-mode expressions. Arithmetic types are silently converted to type complex, and there are complex versions of the arithmetic operators and most mathematical functions. For example:

int i, j;
double x, y;
complex a, b;
a = sin((b+i)/y) + x/j;

The expression b+i is mixed-mode. Integer i is converted to type complex via the constructor complex::complex(double,double=0), the integer first being converted to type double. The result is to be divided by y, a double, so y is also converted to complex and the complex divide operation is used. The quotient is thus type complex, so the complex sine routine is called, yielding another complex result, and so on.

Not all arithmetic operations and conversions are implicit, or even defined, however. For example, complex numbers are not well-ordered, mathematically speaking, and complex numbers can be compared for equality only.

complex a, b;
a == b; // OK
a != b; // OK
a <  b; // error: operator < cannot be applied to type complex
a >= b; // error: operator >= cannot be applied to type complex

Similarly, there is no automatic conversion from type complex to any other type, because the concept is not well-defined. You can specify whether you want the real part, imaginary part, or magnitude, for example.

complex a;
double f(double);
f(abs(a)); // OK
f(a);      // error: no match for f(complex)