It is an explanation of a theorem in radius of convergence of power series. ∞ ∞ Theorem:- ∑ anzn is a power series and ∑ nanzn – 1 is the power series obtained n=0 n=0 by differentiating the first series term by term. Then the derived series has the same radius of convergence as the original series.

Complex Variable Radius of Convergence of the Power Series ∞ ∞ Theorem:- ∑ anzn is a power series and ∑ nanzn – 1 is the power series obtained n=0 n=0 ... click for more

It is an explanation of a theorem in radius of convergence of power series. ∞ ∞ Theorem:- ∑ anzn is a power series and ∑ nanzn – 1 is the power series obtained n=0 n=0 by differentiating the first series term by term. Then the derived series has the same radius of convergence as the original series.

Complex Variable Radius of Convergence of the Power Series ∞ ∞ Theorem:- ∑ anzn is a power series and ∑ nanzn – 1 is the power series obtained n=0 n=0 ... click for more

Linear Transformations; Polar and Rectangular Coordiantes

Find the region onto which the half plan y > 0 is mapped by the transformation ... Please see attachment for complete question. Thanks!

Semi-Infinite Strip

Find the image of the semi-infinite strip x > 0, 0 < y < 2 when w = iz + 1. Sketch the strip and its image ... {see attachment}

Half Plane Under Given Transformation ...

2. Show that when {see attachment}, the image of the half plan {see attachment{ under ther transformation w = 1/z is the interior of a circle. What is the image when {see attachment}?