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I am trying to solve the following problem: $\\$ $\lim_{z \rightarrow i}\dfrac{z^2 + i}{z^4 - 1}$

I have tried everything I can think of to solve this problem (rationalizing, factoring, polar form, etc.). Any help would be greatly appreciated.

I looked in the back of the book, because I believed it to be undefined, and it said that the answer is $-\frac{1}{2}$.

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    What are the respective limits of numerator and denominator? – 2017-01-27
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    Looks undefined to me since direct substitution gives $\dfrac{-1+i}0$. In the single-variable (real) case this generally means the limit is undefined. Pretty sure it's the same in the complex case (which is more or less a two-variable real case) but can't recall completely. – 2017-01-27
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    @tilper In complex analysis, one typically uses the Riemann sphere (aka the complex projective line), and then we have an unambiguous limit of $\infty$. At the beginning of the course, before the introduction of the Riemann sphere, it may be considered nonexistent, though. – 2017-01-27
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    Can we use L'Hospital Rule here? – 2017-01-27
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    @ Subhash Chand Bhoria : it is not $$\dfrac00$$ – 2017-01-27
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    The answer is supposedly $\frac {-1}{2}$ – 2017-01-27

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