I was supposed to have learnt this in my first year but i seem to have forgotten it because i havent kept in touch with it(adsbygoogle = window.adsbygoogle || []).push({});

Definition:A sequence of complex numbers [itex] \left{z_{n}\right}_{1}^{\infty} [/itex] is said to have the limit Z0 or to converge to Zo and we write [tex] \lim_{n \rightarrow \infty} z_{n} = z_{0} [/tex] if for any epsilon>0 there exists an integer N such taht |Zn-Zo|< epsilon for all n>N

Using the given definition prove that the sequence of complex number

Zn = Xn + iYn converges to Zo = Xo + iYo iff Xn converges to Xo and Yn converges to Yo.

[Hint: |Xn - Xo|<=|Zn - Zo|

|Yn - Yo|<=|Zn-Zo|

|Zn - Zo|<=|Xn - Xo|+|Yn - Yo|

so we suppose the first part that

Zn = Xn + iYn converges to Zo = Xo + iYo then Xn converges to Xo and Yn converges to Yo.

well suppose it was triue then

[tex] |Z_{n} - Z_{0}| = |X_{n} - X_{0} + iY_{n} - iY_{0}| \leq |X_{n} - X_{0}| + i|Y_{n} - Y_{0}| < \delta_{1} + \delta_{2} < \epsilon [/tex]

not sure how to choose the pepsilon... do i make it the min of delta1 and delta 2 or the max?

for the other way around i get that easily

your help is greatly appreciated!

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# Homework Help: Simple calculus proof

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