Introduction

Question 1

Im(z)

Answer 1

z-ż/2i

Question 2

Convergence of sequences

Answer 2

The sequence zn of complex numbers converges to the complex number z of for all ε>0 there exists N st n>N |zn-z|

Question 3

Cauchy Sequence

Answer 3

Given ε>0 I can find an N st m,n>N then we have |zn-zm|

Question 4

Open disk

Answer 4

D(z0,ε)={zEc, |z-z0| St D(z,r)Cs

Question 5

Punctured Disk

Answer 5

D’(z0,ε)={zEC st 0

Question 6

Polygonally Connected

Answer 6

A set S is Polygonally connected if for any point z,wES I can find a polygonal path (a union of a sequence of line segments starting at z and finished at w) contained is S jointing z and w

Question 7

Domain/Region

Answer 7

An open set which is Polygonally connected

Question 8

Holomorphic conditions

Answer 8

u and v are continuous on D
The CRE exist and are continuous on D
The CRE hold at z0

If f is holomorphic the u and v are harmonic

Question 9

Re(z)

Answer 9

z+ż/2

Question 10

Simple Curve

Answer 10

A curve f is called simple if it’s image does not cross itself (apart from the end points)

Question 11

Contour

Answer 11

A simple closed path