Theorem 2.2. Suppose that and . Then
Proof.
Proof of Theorem 2.3 is left as an exercise in the book.
Complex Analysis for Mathematics and Engineering
(c) 2006 John H. Mathews, Russell W. Howell
![[Graphics:Images/ComplexFunLimitMod_gr_172.gif]](../Images/ComplexFunLimitMod_gr_172.gif){kind=small}
and ![[Graphics:Images/ComplexFunLimitMod_gr_173.gif]](../Images/ComplexFunLimitMod_gr_173.gif){kind=small}
. Then ![[Graphics:Images/ComplexFunLimitMod_gr_174.gif]](../Images/ComplexFunLimitMod_gr_174.gif)
and . Then