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$\lim_{z\to 0}\frac{\bar z} z$

I think that the limit is 1 but i'm not sure how to show that

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    I'm not sure what you mean by exponential for, do you mean x-iy/x+iy2012-11-03

1 Answers 1

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$\lim_{z\to 0}\frac{\bar z} z$ does not exist: approaching zero on the real axis gives you a limit $1$ and approaching on the imaginary axis gives $-1$.

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    It would certainly be safer to give some details. One possibility is to use the definition of limit directly. Another way is to construct two sequences $x_n$ and $y_n$ such that $x_n,y_n\to 0$ as $n\to\infty$ but $\overline{x_n}/x_n\to 1$ and $\overline{y_n}/y_n\to -1$.2012-11-04