91Ó°ÊÓ

In Exercises 1-4, find real numbers \(a\) and \(b\) such that the equation is true. $$ a+b i=13+4 i $$

Graphical and Analytical Analysis In Exercises 27-30, (a) use a graphing utility to graph the function, (b) find all the zeros of the function, and (c) describe the relationship between the number of real zeros and the number of \(x\)-intercepts of the graph. $$ f(x)=x^{3}-4 x^{2}+x-4 $$

In Exercises 57-62, find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) $$ 1,5 i,-5 i $$

In Exercises 59-66, (a) write the trigonometric forms of the complex numbers, (b) perform the indicated operation using the trigonometric forms, and (c) perform the indicated operation using the standard forms, and check your result with that of part (b). $$ \frac{5}{2+3 i} $$

In Exercises 65-74, use the Quadratic Formula to solve the quadratic equation. $$ \frac{7}{8} x^{2}-\frac{3}{4} x+\frac{5}{16}=0 $$

In Exercises 97-100, solve the equation and check your solution. $$ -x-12=19 $$