Comment by rdtsc

You can try it out in Python directly which natively support complex numbers (just use j instead of i):

   >>> import math
   >>> z=1+2j
   >>> z*complex.conjugate(z)
   (5+0j)
   >>> math.sqrt((z*complex.conjugate(z)).real)
   2.23606797749979
   >>> abs(z)
   2.23606797749979

As we can see abs(z) does the right thing. Try it with a negative imaginary part too and "nicer" values:

   >> z = 3-4j
   >>> math.sqrt((z*complex.conjugate(z)).real)
   5.0
   >>> abs(z)
   5.0