(iv) z2+4z+13=0 z^2 + 4z + 13 = 0z2+4z+13=0 Solution Isolate the constant term:z2+4z=−13Add (42)2=(2)2=4 to both sides:z2+4z+4=−13+4(z+2)2=−9Take square root:z+2=±−9=±3iz=−2±3i\begin{aligned} & \boxed{\text{Isolate the constant term:}} \\ \\ & z^2 + 4z = -13 \\ \\ & \boxed{\text{Add } \left(\frac{4}{2}\right)^2 = (2)^2 = 4 \text{ to both sides:}} \\ \\ & z^2 + 4z + 4 = -13 + 4 \\ \\ & (z + 2)^2 = -9 \\ \\ & \boxed{\text{Take square root:}} \\ \\ & z + 2 = \pm \sqrt{-9} = \pm 3i \\ \\ & z = -2 \pm 3i \end{aligned}Isolate the constant term:z2+4z=−13Add (24)2=(2)2=4 to both sides:z2+4z+4=−13+4(z+2)2=−9Take square root:z+2=±−9=±3iz=−2±3i