1.
Let Z1Z_1 and Z2Z_2 be two complex numbers such that arg(Z1Z2)=π4\arg(Z_1 - Z_2) = \frac{\pi}{4} and Z1,Z2Z_1, Z_2 satisfy the equation z3=Re(z)|z - 3| = \operatorname{Re}(z). Then the imaginary part of Z1+Z2Z_1 + Z_2 is equal to