c# - product of double.PositiveInfinity and i -

i ran following strange product in c#. test below passes.

public void infinitytimesitest() {   complex infinity = new complex(double.positiveinfinity, 0);   complex = new complex(0, 1);   complex product = infinity * i;   double real = product.real;   double imaginary = product.imaginary;   assert.isnan(real);   assert.istrue(double.ispositiveinfinity(imaginary)); } 

it passes if reverse order of terms in product. thinking mathematically, c# appears saying is:

 infinity * = (real nan) + infinity * i. 

that seems strange choice. there must thinking behind it. i'm hoping here can provide insight going on.

i think expands complex multiplication this:

(inf + 0i) * (0 + i) = inf * 0 + inf * + 0i * 0 + 0i * = inf * 0 + inf * 

first term product of infinity , 0 - nan. second term imaginary infinity.

edit: if @ sources, complex multiplication operator looks this:

public static complex operator *(complex left, complex right) {   return new complex(left.m_real * right.m_real - left.m_imaginary * right.m_imaginary, left.m_imaginary * right.m_real + left.m_real * right.m_imaginary); }