91Ó°ÊÓ

Surface area of a cylinder: \(A=2 \pi r^{2}+2 \pi r h\) The surface area of a cylinder is given by the formula shown, where \(h\) is the height and \(r\) is the radius of the base. The equation can be considered a quadratic in the variable \(r\). Use the quadratic formula to solve for \(r\) in terms of \(h\) and \(A\) (Hint: Rewrite the equation in standard form and identify the coefficients as before.)

Complex polynomials: Many techniques applied to solve polynomial equations with real coefficients can be applied to solve polynomial equations with complex coefficients. Here we apply the idea to carefully chosen quadratic equations, as a more general application must wait until a future course, when the square root of a complex number is fully developed. Solve each equation using the quadratic formula, noting that \(\frac{1}{i}=-i\). $$0.5 z^{2}+(4-3 i) z+(-9-12 i)=0$$