Answer to Question #50127 in Complex Analysis for tota

Question #50127

Show that if
∑ Zn is convergent , then ∑ Zn ^ 2 is also convergent

please more than method

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Assignment Expert

06.01.15, 16:59

Dear Tota. Using provided reasonings in the solution, you can prove your statement, because it holds for positive real numbers and for absolute value of purely imagine numbers (Ai, where A is real), taking into account that any complex number can be represented as the sum of real and purely imagine number, square root of a sum is less than the sum of absolute value of each term.

Assignment Expert

29.12.14, 18:43

Dear vallle. Thank you for adding information.

vallle

29.12.14, 17:27

you are right , i missed word { absolutely} convergent for the first series Zn then Zn^2 is convergent . Sorry

Tota

29.12.14, 17:19

Sorry Sorry , I missed one word { Absolutely } before convergent of Zn in the first Series should Absolutely convergent Really appreciate your reply