Strip

The set of points in a plane between two parallel straight lines in this plane. The coordinates $ x , y $ of a point in a strip satisfy inequalities $ C _ {1} < Ax + By < C _ {2} $, where $ A $, $ B $, $ C _ {1} $, $ C _ {2} $ are certain constants with $ A $ and $ B $ not both equal to zero. The function $ w = e ^ {z} $ maps the strip $ 0 < y < \pi $ in the complex plane $ ( z = x + iy ) $ conformally onto the upper half-plane of the complex $ w $- plane.

References

[a1]	R.V. Churchill, J.W. Brown, R.F. Verhey, "Complex variables and applications" , McGraw-Hill (1974)