(i) 2z4−32=02z^4 - 32 = 02z4−32=0 Solution Factor out common factor 2:2(z4−16)=0 ⟹ z4−16=0Difference of squares: a2−b2=(a−b)(a+b)(z2−4)(z2+4)=0Apply zero product property:z2−4=0orz2+4=0z2=4 ⟹ z=±2z2=−4 ⟹ z=±2iTherefore: z=2,−2,2i,−2i\begin{aligned} & \boxed{\text{Factor out common factor 2:}} \\ \\ & 2(z^4 - 16) = 0 \implies z^4 - 16 = 0 \\ \\ & \boxed{\text{Difference of squares: } a^2 - b^2 = (a - b)(a + b)} \\ \\ & (z^2 - 4)(z^2 + 4) = 0 \\ \\ & \boxed{\text{Apply zero product property:}} \\ \\ & z^2 - 4 = 0 \quad \text{or} \quad z^2 + 4 = 0 \\ \\ & z^2 = 4 \implies z = \pm 2 \\ \\ & z^2 = -4 \implies z = \pm 2i \\ \\ & \boxed{\text{Therefore: } z = 2, -2, 2i, -2i} \end{aligned}Factor out common factor 2:2(z4−16)=0⟹z4−16=0Difference of squares: a2−b2=(a−b)(a+b)(z2−4)(z2+4)=0Apply zero product property:z2−4=0orz2+4=0z2=4⟹z=±2z2=−4⟹z=±2iTherefore: z=2,−2,2i,−2i