Problem 47003. Combine complex conjugates first when computing the product of vector

Richard Allred

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Analytically, the product of complex conjugates yields a real result.  When numerically computing the product of a vector containing large valued complex conjugates, care must be taken to ensure that the terms are first multiplied with their conjugate to ensure that the result is real.
For example:
v = [ -376565273.869706 +                     0i
      -3419197614.44981 +      1946408802.27484i
      -3419197614.44981 -      1946408802.27484i
      -3789372834.14304 +      4660481826.64665i
      -3789372834.14304 -      4660481826.64665i
      -4853975182.33591 +      6452212202.13479i
      -4853975182.33591 -      6452212202.13479i];
prod(v) = -1.37103891526544e+67 +  2.24486651494027e+51i
Combine the vector's terms together in such a way that the product is real.