Answer:
-i/2
Step-by-step explanation:
Recall that i² = -1.
z² + 1 factors into (z + i)(z - i), and so the original expression reduces as follows:
z - i 1
--------------- = --------- for z not equal to i
(z + i)(z - i) z + i
Now attempt to find the limit as z approaches i of the above rational fraction. The limit is
1 1 1
--------- = ------ which, if rationalized, becomes ------- (-i), or -i/2
i + i 2i 2
