Let \((a_1,b_1), (a_2,b_2), \dots, (a_n,b_n)\) be all the ordered pairs \((a,b)\) of complex numbers with \(a^2+b^2\neq 0, a+\frac{10b}{a^2+b^2}=5, \text{ and } b+\frac{10a}{a^2+b^2}=4.\) Find \(a_1 + b_1 + a_2 + b_2 + \dots + a_n + b_n.\)
The answer is 33.
+99 
