It's complicated

Algebra Level 5

\[ a+\frac{a+8b}{a^{2}+b^{2}}=2 \text{ and } b+\frac{8a -b}{a^{2}+b^{2}}=0. \]

Give the sum of the elements in all ordered pairs of real numbers \((a, b)\) such that the two equations above are satisfied.

Hint: Sometimes, you have to make the problem more complex to solve it.

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