(iii) ∣−7z2+2z2ˉ∣|-7z_2+2\bar{z_2}|∣−7z2+2z2ˉ∣ Solution Given z2=−5+3i ⇒ z2ˉ=−5−3i.−7z2=−7(−5+3i)=35−21i2z2ˉ=2(−5−3i)=−10−6i−7z2+2z2ˉ=(35−21i)+(−10−6i)=25−27i∣−7z2+2z2ˉ∣=∣25−27i∣=252+(−27)2=1354\begin{aligned} & \boxed{\text{Given } z_2=-5+3i\ \Rightarrow\ \bar{z_2}=-5-3i.} \\ \\ & -7z_2=-7(-5+3i)=35-21i \\ & 2\bar{z_2}=2(-5-3i)=-10-6i \\ \\ & -7z_2+2\bar{z_2}=(35-21i)+(-10-6i)=25-27i \\ \\ & |-7z_2+2\bar{z_2}|=|25-27i|=\sqrt{25^2+(-27)^2}=\sqrt{1354} \end{aligned}Given z2=−5+3i ⇒ z2ˉ=−5−3i.−7z2=−7(−5+3i)=35−21i2z2ˉ=2(−5−3i)=−10−6i−7z2+2z2ˉ=(35−21i)+(−10−6i)=25−27i∣−7z2+2z2ˉ∣=∣25−27i∣=252+(−27)2=1354