Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6,$ then what is $a^3 + b^3?$
a + b = 4 square both sides
a^2 + 2ab + b^2 =16
a^2 + b^2 + 2ab = 16
6 + 2ab = 16
2ab = 10
ab = 5
a^3 + b^3 = (a + b) (a^2 + b^2 - ab) = (4) (6 - 5) = 4
+1839 
