Originally Posted by

**avicenna** Thanks for your reply,

Yes, Chrichill and Brown (the book I am using) does have proofs of the theorems you have mentioned in the set of complex numbers and indeed proving the given statement using those theorems is trivial. But I need to solve the question using the basic epsilon delta notation only, without the using the theorms on limits of polynomials or limits of functions multiplied/added together.

I try to work backwards from what I am trying to show ( i.e. for all z such that 0<mod[z-a]<Delta, mod[(z^2+c)-(a^2+c)] < Epsilon), I use the triangle inequality a few times and arrive at a Delta. When I try to then work forward from that Delta to construct a step-by-step proof, that my Delta would indeed leed to the statement that I am trying to prove, it does not work. No matter how I construct the Delta (I have tried a few different ways), I cannot work forward to the statement:

for all z such that 0<mod[z-a]<Delta, mod[(z^2+c)-(a^2+c)] < Epsilon

Can anyone help, or otherwise convince me that I cannot do without employ the theorems of limits mentioned in the post.

Thanks a lot