Find all complex numbers z such that |z|^2 + 2z = 31 - 8i.
Let \(z = a + bi \)
\((a^2-b^2) + 2abi + 2a + 2bi = 31 - 8i\)
Separate real and imaginary components.
\(a^2-b^2 + 2a = 31\)
\(2ab+2b=-8\)
+1223 
