(ii) z2−6z+30=0z^2 - 6z + 30 = 0z2−6z+30=0 Solution Isolate the constant term:z2−6z=−30Add (−62)2=(−3)2=9 to both sides:z2−6z+9=−30+9(z−3)2=−21Take square root:z−3=±−21=±i21z=3±i21\begin{aligned} & \boxed{\text{Isolate the constant term:}} \\ \\ & z^2 - 6z = -30 \\ \\ & \boxed{\text{Add } \left(\frac{-6}{2}\right)^2 = (-3)^2 = 9 \text{ to both sides:}} \\ \\ & z^2 - 6z + 9 = -30 + 9 \\ \\ & (z - 3)^2 = -21 \\ \\ & \boxed{\text{Take square root:}} \\ \\ & z - 3 = \pm \sqrt{-21} = \pm i\sqrt{21} \\ \\ & z = 3 \pm i\sqrt{21} \end{aligned}Isolate the constant term:z2−6z=−30Add (2−6)2=(−3)2=9 to both sides:z2−6z+9=−30+9(z−3)2=−21Take square root:z−3=±−21=±i21z=3±i21