http://img254.imageshack.us/img254/3411/45336636.jpg

I just wanted to know why the signs for the mesh current equation are what they are.

The mesh equation for loop gabg1g is

1(I+Is) - j/0.5(I+Ig) - j(I+2I1) = 0

.

 

The choice of current direction is arbitrary, so it doesn't matter if you have it clockwise or anti-clockwise so long as you maintain the same standard in every equation involving that current.

Then whether its positive or negative result will tell you the actual direction the current is swirling

 

looking at your circuit, by changing some of the current directions they have made it easier for you as the two currents in each component are always in the same direction, very handy!