(iv) z3−5z2+z−5=0z^3 - 5z^2 + z - 5 = 0z3−5z2+z−5=0 Solution Group terms:(z3−5z2)+(z−5)=z2(z−5)+1(z−5)Factor out (z−5):=(z−5)(z2+1)=0Apply zero product property:z−5=0 ⟹ z=5z2+1=0 ⟹ z2=−1 ⟹ z=±iTherefore: z=5,i,−i\begin{aligned} & \boxed{\text{Group terms:}} \\ \\ & (z^3 - 5z^2) + (z - 5) = z^2(z - 5) + 1(z - 5) \\ \\ & \boxed{\text{Factor out } (z - 5):} \\ \\ & = (z - 5)(z^2 + 1) = 0 \\ \\ & \boxed{\text{Apply zero product property:}} \\ \\ & z - 5 = 0 \implies z = 5 \\ \\ & z^2 + 1 = 0 \implies z^2 = -1 \implies z = \pm i \\ \\ & \boxed{\text{Therefore: } z = 5, i, -i} \end{aligned}Group terms:(z3−5z2)+(z−5)=z2(z−5)+1(z−5)Factor out (z−5):=(z−5)(z2+1)=0Apply zero product property:z−5=0⟹z=5z2+1=0⟹z2=−1⟹z=±iTherefore: z=5,i,−i