Complex analysis, find the image of a transformation

Find the image of the region 0<x<1 under the transformation $T: z \to iz$ .
Attempt: I write z=a+ib where 0<a<1 and b can be any real number. So the transformation takes these z and output i(a+ib)=-b+ia.
On the complex plane that makes an infinite horizontal region bounded above by i and below by 0?
While the original graph would be an infinite vertical region bounded on the right by 1 and on the left by 0.
Am I right? I'm quite rusty, I'm trying to end my vacations by starting maths back.
Thanks for any insight.

Sounds right to me. Multiplication by i is a counter-clockwise rotation by $\pi/2$ , if that helps your understanding.

Ok thank you. You're right, I had "forgotten" that a multiplication by i has a rotation effect.