IIT JEE , AIEEE Forum - Mathematics , Algebra

waterdemon

I think that it must be when

f(z) divided by (z-i) and (z+i)

f(i)=i

f(-i)=1+i

on dividing f(z) z^2+1 ;we will get a equation as remainder

let g(z) be quotient & az +b as remainder

f(z)=g(z).(z^2+1) + az+b

f(z)=g(z).(z+i)*(z-i) + az+b

f(i) = ai + b = i

f(-i) = -ai + b=1+i

On soling the equations given above we will get :-

b=(1+2i)/2 and a=-1/2i=i/2

remainder=(i.z)/2+1/2+i

remainder= zi/2 + (1/2 +i).

Hope you get it .

Cheers!!!!!!!!!!!!!!!!!!!!