Product of an array of infinity by an array of zeros gives me an array of NaN

Question

I want to multiply an array of infinity by another array of zeros using Eigen library:

Eigen::ArrayXd a(2); a << INFINITY, INFINITY;
Eigen::ArrayXd b(2); b << 0.000, 0.000;

The result gives me:

std::cout<a*b<<std::endl;

The output is

nan
nan

Why I don't get a vector of zeros?