Complex number convergence

[Rosebud]

Hi. Could someone help me with this question.
I've attached the file. Its part i) of the question.

I know I need the definition of what it means for a sequence to converge which I have.. im still not sure how to answer the question.

Many thanks.

 

[pka]

Recall that a complex number has the form $z=a+bi$ where both $a~\&~b$ are real numbers.
So $|a|=|\Re(z)|\le|z|~\&~|b|=|\Im(z)|\le|z|$.
Consider the sequence $z_n=x_n+y_ni\to a+bi$
Now you need to show that $\overline{z_n}=\overline{x_n+y_i}=x_n-y_ni$.
Using the above show $x_n\to a~\&~y_n\to -b$
I hope that I understood what you asked.

 

[Rosebud]

Thank you that helps a lot