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about to only mathematics

A

`(1)/(2)(z+1)+i`

B

`(1)/(2)(iz +1)+i`

C

`(1)/(2)(iz-1)+i`

D

`(1)/(2)(z+i)+1`

Text Solution

Verified by Experts

The correct Answer is:
B
`f(z) = g(z)(z-i) (z+i) + az + b,a, b in C`
Given , `f(i) = i`
`rArr ai + b = i`
` and f(-i) = 1 +i`
`rArr a(-i) +b = 1 +i`
From (1) and (2), we have
`a= (i)/(2), b= (1)/(2)+i`
Hence, the required remaider is `az + b = (1//2)iz + (1//2) + i` .
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