Let z_1 and z_2 be two complex numbers such that arg (z_1-z_2)=(π)/4 and z_1, z_2 satisfy the equation |z-3|= Re (z). Then the imaginary part of…

Let $\displaystyle z_1$ and $\displaystyle z_2$ be two complex numbers such that arg $\displaystyle \left(z_1-z_2\right)=\frac{\pi}{4}$ and $\displaystyle z_1, z_2$ satisfy the equation $\displaystyle |z-3|=\operatorname{Re}(z)$. Then the imaginary part of $\displaystyle z_1+z_2$ is equal to \_\_\_\_.