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If the remainders respectively when `f(z) = z^(3)+z^(2)+2z+1` is divided with `z-i` and `z+i` and `1+3i` and `1+i` then find the remainder when `f(z)` is divided with `z^(2)+1` ?

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The correct Answer is:
`z+1+2i`
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AAKASH SERIES-PARTIAL FRACTIONS-PRACTICE EXERCISE
  1. If the remainders respectively when f(z) = z^(3)+z^(2)+2z+1 is divided...

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  2. The remainder obtained when the polynomial x^(4)-3x^(3)+9x^(2)-27x+81 ...

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  3. If the remainder of the polynomial f(x) when divided by x+1 and x-1 ar...

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  4. If (3x+4)/(x^(2)-3x+2)=A/(x-2)-B/(x-1) then (A, B) =

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  5. If (1-x+6x^(2))/(x-x^(3))=A/x +(B)/(1-x)+(C)/(1+x), then A=

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  6. If (x^(2)+5)/(x^(2)+2)^(2)=1/(x^(2)+2)+k/(x^(2)+2)^(2) " then " k=

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  7. If (x+1)/((x-a)(x-3))=2/(x-a)+b/(x-3), " then "(a, b)=

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  8. (2x-1)/((x-1)(2x+3))=1/(5(x-1))-k/(5(2x+3)), then k =

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  9. If (x^(2)-10x+13)/((x-1)(x^(2)-5x+6))=A/(x-1)+B/(x-2)+C/(x-3), then C ...

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  10. if (5x^(2) +2)/(x^(3)+x)=(A(1))/(x)+(A(2)x+A(3))/(x^(2)+1), then (A(...

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  11. If (x^(3))/((x-a)(x-b)(x-c))=1 +(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then A=

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  12. If (x^(4))/((x-1)(x-2))=x^(2)+3x+7+(A)/(x-2)+(B)/(x-1) then A=

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  13. ((x+1))/((2x-1)(3x+1))=A/((2x-1))+B/((3x+1)) rArr 16A+9B=

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  14. If (x^(2)+1)/((x^(2)+2)(x^(2)+3))=(A)/(x^(2)+3)+(B)/(x^(2)+2) then (A,...

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  15. If (x^(2)+x+1)/(x^(2)+2x+1)=A+B/(x+1)+C/(x+1)^(2) then A - B =

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  16. If (x^(2)-5x+7)/(x-1)^(3)=A/(x-1)+B/(x-1)^(2)+C/(x-1)^(3) " then " A+B...

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  17. Resolve the following into partial fractions. (3x^(2)-8x^(2) + 10)/(...

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  18. If (2x^(2)+5)/((x+1)^(2)(x-3))=(A)/(x+1)+(B)/((x+1)^(2))+(C)(x-3) then...

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  19. The partial fractions of (1)/(x^(2)(x+2)) are

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  20. If (x^(4))/((x-1)(x-2)(x-3))= A.x+B. (1)/((x-1))+C (1)/((x-2))+D. (1)/...

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  21. If (2x^(2)+3x+4)/((x-1)(x^(2)+2))=A/(x-1)+(Bx+C)/(x^(2)+2), " then "B=

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