(ii) 3z5−243z=03z^5 - 243z = 0 3z5−243z=0 Solution Factor out common factor 3z:3z(z4−81)=0Apply zero product property:3z=0 ⟹ z=0z4−81=0 ⟹ z4=81Difference of squares:(z2−9)(z2+9)=0z2−9=0 ⟹ z2=9 ⟹ z=±3z2+9=0 ⟹ z2=−9 ⟹ z=±3iTherefore: z=0,3,−3,3i,−3i\begin{aligned} & \boxed{\text{Factor out common factor 3z:}} \\ \\ & 3z(z^4 - 81) = 0 \\ \\ & \boxed{\text{Apply zero product property:}} \\ \\ & 3z = 0 \implies z = 0 \\ \\ & z^4 - 81 = 0 \implies z^4 = 81 \\ \\ & \boxed{\text{Difference of squares:}} \\ \\ & (z^2 - 9)(z^2 + 9) = 0 \\ \\ & z^2 - 9 = 0 \implies z^2 = 9 \implies z = \pm 3 \\ \\ & z^2 + 9 = 0 \implies z^2 = -9 \implies z = \pm 3i \\ \\ & \boxed{\text{Therefore: } z = 0, 3, -3, 3i, -3i} \end{aligned}Factor out common factor 3z:3z(z4−81)=0Apply zero product property:3z=0⟹z=0z4−81=0⟹z4=81Difference of squares:(z2−9)(z2+9)=0z2−9=0⟹z2=9⟹z=±3z2+9=0⟹z2=−9⟹z=±3iTherefore: z=0,3,−3,3i,−3i