# 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.