# 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: $$i=\sqrt{-1}$$ .

×