(ii) ∣3z1+2z2∣|3z_1+2z_2|∣3z1+2z2∣ Solution Given z1=2+7i, z2=−5+3i.3z1=3(2+7i)=6+21i2z2=2(−5+3i)=−10+6i3z1+2z2=(6+21i)+(−10+6i)=−4+27i∣3z1+2z2∣=∣−4+27i∣=(−4)2+272=745\begin{aligned} & \boxed{\text{Given } z_1=2+7i,\ z_2=-5+3i.} \\ \\ & 3z_1=3(2+7i)=6+21i \\ & 2z_2=2(-5+3i)=-10+6i \\ \\ & 3z_1+2z_2=(6+21i)+(-10+6i)=-4+27i \\ \\ & |3z_1+2z_2|=|-4+27i|=\sqrt{(-4)^2+27^2}=\sqrt{745} \end{aligned}Given z1=2+7i, z2=−5+3i.3z1=3(2+7i)=6+21i2z2=2(−5+3i)=−10+6i3z1+2z2=(6+21i)+(−10+6i)=−4+27i∣3z1+2z2∣=∣−4+27i∣=(−4)2+272=745