sketch given region an its image under given mapping
$2 \leq Im z \leq 5$ and $w=iz$
Here is what I got so far
$z=x+iy$ so $2\leq y\leq 5$ and $w=-y+ix$ sp $-5+ix \leq w \leq 2+ix$
this implies that $-5 \leq Re( w) \leq -2$. But the answer is the back of the book says the answer is $-5 \leq Re(z) \leq -2$. I'm not sure I understand how they got this, and I don't understand how they determine the image from this.
I understand that this map send a disk with radius $1$ to another unit disk. I wonder if anyone would please explain this very carefully for me please. I really want to understand conformal mapping stuff.