I don't understand why conjugate is taken. How do I interpret it?
208k 48 48 gold badges 571 571 silver badges 2.3k 2.3k bronze badges asked Apr 2, 2013 at 14:11 487 1 1 gold badge 8 8 silver badges 15 15 bronze badgesIn this problem complex numbers are being used as a notation for 2-dimensional vectors.
The dot product of two vectors is defined by $(a,b)\cdot(c,d)=ac+bd$ but it can also be written as $\Re((\overline)(c+id)) = \Re((a-ib)(c+id)) = ac+bd$.
The solution is using this trick to write $F\cdot z$ as $\Re(\bardz)$.
(The notation in the solution seems a little confused to me. It probably should say $\Re\int_C\bardz$ instead of $\Re\int_C\bar\cdot dz$. Because either you're using dot products, or you're using complex numbers, but not (in this case) both. But that's a minor quibble.)
