Dividing f(z) by z−i, we get the remainder i and dividing it by z+i, we get the remainder 1+i. Find the remainder upon the division of f(z) by z²+1.
A. 1/2iz + 1/2 + i
B. 1/2z + 1/2 - i
c. 1/2iz + 1/2 - i
d. 1/2z + 1/2 + i