# Compute the given complex limit of limz→i(ln|x2+y2|+iarctan(yx))limz→i(ln|x2+y2|+iarctan(yx))\lim_{z \rightarrow i}(\ln|x^2+y^2| + i\arctan(\frac{y}{x}))

Compute the given complex limit of limz→i(ln|x2+y2|+iarctan(yx))\lim_{z \rightarrow i}(\ln|x^2+y^2| + i\arctan(\frac{y}{x}))

I can see that this reduces to lim(x,y)→(0,1)(ln|x2+y2|+iarctan(yx))\lim_{(x,y) \rightarrow (0,1)} (\ln|x^2+y^2|+ i\arctan(\frac{y}{x})). The real part of the complex expression is 00, but I’m having trouble understanding what I would do for the complex part. This seems to be just θ\theta as the angle of ii which would be π/2\pi/2, but am I missing something here?

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