1- 2 all parts HW 2.2.1: Complex Roots Visualization They 10/3/ 29 1. Consider the graph of f (x) = x -4x+5 on a. Graph f (x) in detail in the xy-plane of the coordinate system provided without using a calculator. b. What conclusion can you make about the -5 -4 -3 -2 -1 2 4 5 roots of f (x ) ? in two N to c. Show that 2 - i is a root for f (x). d. Show that f(2-31) is a real number. e. Show that f (3+ i) is not a real number. f. Try a few more complex values and make a conjecture about values of a and b for which f(a+ bi) is a real number. Explain how you arrived at your conjecture and prove that it is true. g. Lastly, draw a graphical representation of what your above answer implies about the real-valued outputs of f with regard to the inclusion of a complex domain. y X i2. Consider the graph of f(x)=x +8x +18 a. Graph f(x) in detail in the xy-plane of the coordinate system provided without using a calculator. b. What conclusion can you make about the roots of f (x) ? - 5 - 2 2 3 4 5 in bwN to C. Show that -4 + V27 is a root for f(x) d. Show that f(-4-37) is a real number. e. Show that f (3+ 2i) is not a real number. Teamuniser son al (yet jy ten world. s f. Try a few more complex values and make a conjecture about values of a and b for which f(a+ bi) is a real number. Explain how you arrived at your conjecture and prove that it is true. g. Lastly, draw a graphical representation of what your above answer implies about the real-valued outputs of fwith regard to the inclusion of a complex domain. y X i