Notice that if , then . This represents a reflection about the Real axis.
Then , which represents a complete reflection about both the Imaginary and Real axes. So by symmetry, in the second quadrant you end up with the same angle as in the first quadrant but swept out in a clockwise direction from the negative real axis. If we were to measure this angle from the positive real axis in the anticlockwise direction (as we normally do), then it's the same as subtracting that reference angle from .
Say our angle had been . When we perform the transformations to to get , you should find you get , which is NOT a rotation of from .
To answer your second question, you should know that and . So