Complex Numbers

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