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Math Help - Complex Limit

  1. #1
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    Complex Limit

    Consider the Limit \displaystyle \lim_{z\to i}\left[|z|+iArg(iz)\right].

    What is the limit when approaching i on the unit circle in the first quadrant?

    \displaystyle \lim_{z\to i}|z|+\lim_{z\to i}iArg(iz)\rightarrow 1+\lim_{\theta\to \frac{\pi}{2}}-\theta\rightarrow 1-\frac{\pi}{2}

    Is this correct?
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  2. #2
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    No.

    \displaystyle \lim_{z \to i}i\arg{(iz)} = i\arg{(i^2)} = i\arg{(-1)} = \pi i.
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