\(a+\sqrt{b}\), its conjugate: \(a-\sqrt{b}\)
If their sum is -4:
\(a+\sqrt{b}+a-\sqrt{b}=-4 \implies 2a=-4 \implies a=-2\)
If their product is 1:
\((2+\sqrt{b})(2-\sqrt{b})=1 \iff 4-2\sqrt{b}+2\sqrt{b}-b=1\)
So:
\(4-b=1 \implies b=3\)
Therefore, \(a+b=-2+3=1\)
+140 
