1.
Let a,ba, b be two non-zero real numbers. Then the number of elements in the set X={zC:Re(az2+bz)=a and Re(bz2+az)=b}X = \{z \in \mathbb{C} : \text{Re}(az^2 + bz) = a \text{ and } \text{Re}(bz^2 + az) = b\} is equal to: