Is this package somehow defeating perl's normal error-reporting mechanisms?

No, the messages are warnings, not errors (i.e. exceptions). They appear because Math::Complex invokes the warnings pragma on line 73 of the source code (version 1.59).

Carp::Always will display the line number you are seeking. But it won’t produce a stack trace, because no exception is thrown:

 3:06 >perl 573_SoPW.pl
Use of uninitialized value $z2 in multiplication (*) at C:\Perl\lib\pe
+rl5/Math/Complex.pm line 489.
        Math::Complex::_multiply('Math::Complex=HASH(0x186e5e4)', unde
+f, '') called at 573_SoPW.pl line 5
Use of uninitialized value $z2 in multiplication (*) at C:\Perl\lib\pe
+rl5/Math/Complex.pm line 489.
        Math::Complex::_multiply('Math::Complex=HASH(0x186e5e4)', unde
+f, '') called at 573_SoPW.pl line 5
0
 3:06 >
[download]

Hope that helps,