(iv) ∣(z1+z2)3∣|(z_1+z_2)^3|∣(z1+z2)3∣ Solution First find z1+z2:z1+z2=(2+7i)+(−5+3i)=−3+10iUse property ∣zn∣=∣z∣n:∣(z1+z2)3∣=∣z1+z2∣3∣z1+z2∣=∣−3+10i∣=(−3)2+102=109∣(z1+z2)3∣=(109)3=109109\begin{aligned} & \boxed{\text{First find } z_1+z_2:} \\ \\ & z_1+z_2=(2+7i)+(-5+3i)=-3+10i \\ \\ & \boxed{\text{Use property } |z^n|=|z|^n:} \\ \\ & |(z_1+z_2)^3|=|z_1+z_2|^3 \\ \\ & |z_1+z_2|=|-3+10i|=\sqrt{(-3)^2+10^2}=\sqrt{109} \\ \\ & |(z_1+z_2)^3|=(\sqrt{109})^3=109\sqrt{109} \end{aligned}First find z1+z2:z1+z2=(2+7i)+(−5+3i)=−3+10iUse property ∣zn∣=∣z∣n:∣(z1+z2)3∣=∣z1+z2∣3∣z1+z2∣=∣−3+10i∣=(−3)2+102=109∣(z1+z2)3∣=(109)3=109109