Bus $1$ with voltage magnitude $V_{1}=1.1 \: pu$ is sending reactive power $Q_{12}$ towards bus $2$ with voltage magnitude $\text{$V_{2}=1$ pu}$ through a lossless transmission line of reactance $X$. Keeping the voltage at bus $2$ fixed at $1 \: pu$, magnitude of voltage at bus $1$ is changed, so that the reactive power $Q_{12}$ sent from bus $1$ is increased by $20 \%$. Real power flow through the line under both the conditions is zero. The new value of the voltage magnitude, $V_{1}$, in $pu$ ( rounded off to $2$ decimal places), at bus $1$ is___________________.
