The complex number _{$\frac{5(i-3)}{1+i}$}  lies in the

_{$\frac{5\left(i-3\right)}{1+i}=\frac{5\left(i-3\right)\left(1-i\right)}{1^2+i^2}$}

              _{$=\frac{5\left(i-3-i^2+3i\right)}{2}$}                 

              _{$=\frac{5\left(-2+4i\right)}{2}$}

              _{$=-5+10i\in Q_2$}