Let $$w = z\bar{z} + k_1z + k_2iz + \lambda(1+i)$$, $$k_1, k_2 \in \mathbb{R}$$. Let $$Re(w) = 0$$ be the circle $$C$$ of radius 1 in the first quadrant touching the line $$y = 1$$ and the $$y$$-axis. If the curve $$Im(w) = 0$$ intersects $$C$$ at $$A$$ and $$B$$, then $$30(AB)^2$$ is equal to _____.