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 \( C \) of radius \( 1 \) in the first quadrant touching the line \( y=1 \) and the y-axis. If the curve \( \operatorname{Im}(w)=0 \) intersects \( C \) at \( A \) and \( B \), then \( 30(AB)^{2} \) is equal to _____.
