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I've been going through a few past papers for an upcoming exam on complex analysis, I found this T/F question with a few parts i'm not confident on, I'll explain the whole lot of my work and show.

[PLAIN]http://img404.imageshack.us/img404/2069/asdasdsu.jpg [Broken]

a) |2+3i|=|2-3i| so false

b) True since when the coefficients are real the roots come in complex conjugate pairs

c) Using triangle inequality, 1/|z^2+1|=> 1/|z^2| +2 = 1/ (x^2+y^2+2)

1/ (x^2+y^2+2)<=1/x^2+2<=1/2 im not sure if these inequality opperations are 100%

d)False, cannot be every f since f must be analytic within the domain and curve region

e) False, i think, by Cauchys integral formula C must be a simple closed curve enclosing Zo, so as C in this question is just a line, False

f) I think this is true, but i'm not sure if you can use cauchys theorem backwards. So true as int f(z)dz=0 if f is analytic in C. So since int f(z)dz=0, f must be analytic inside and on C.

Is the converse of the cauchy theorem true?

h) I'm not sure how to approach this, but I was thinking you could just let an be somthing like 1/sqrt(3)^n for the h), then it would work, true

g) i cant see a way to do somthing similar, so i think the answer is false, since if you make an "an" such that converges for 2-i, then it will also converge for 1+i,

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# Homework Help: Going over complex analysis past exam

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