Apply Partial Fractions With Complex Numbers

Algebra Level 4

\[\large\sum_{x=1}^{10} \dfrac{1}{x^2+x-49+7(2x+1)i}\]

If the above summation in the simplest form can be expressed as \(\dfrac{-(a+ib)}{c}\) where \(a,b,c\) are positive integers and \(\gcd(a,b)=1\) , compute \(a+b+c\) .

Clarification: \(i=\sqrt{-1}\) .

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