1) Can anyone think of a function of a complex variable which is conformal at some points but not at others? Please indicate the point/s at which it is not conformal and the points at which it is.

2) Consider a function of a complex variable and a pointain its domain. Can anyone think of a mapping which preserves angles between two particular curves intersecting atabut for which angle preservation does not occur for all pairs of curves intersecting at the same pointa ?