2. (Roots of unity revisited: adapted from LM 3.1–24) In Problem 2, Homework 1, we calculated all five roots of x 5 + 1, but it required a number of lines of code. In this problem, we will do this more compactly for a more general x n + 1. Recall that −1 = e πi = e 3πi = e 5πi = · · · , but, if we take the nth root, we obtain n distinct values e πi/n, e3πi/n, e5πi/n , . . . , due to the periodicity of the complex exponentials; think Euler. (a) Write a script which, given a positive integer n, finds all n roots of x n + 1 at once, using ONE statement. It must also print out all n of these roots neatly using either disp or fprintf in tabular form. A loop may be used for printing results, but is not allowed in the calculation of the roots. (b) Run the script with n = 3, 5, 7, and 1

Write a program that displays the following menu: geometry calculator 1. calculate the area of a circle 2. calculate the area of a rectangle 3. calculate the area of a triangle 4. quit enter your choice (1-4): if the user enters 1, the program should ask for the radius of the circle and then display its area. use the following formula: area = ď€(the square of r) use 3.14159 for ď€ and the radius of the circle for r. if the user enters 2, the program should ask for the length and width of the rectangle and then display the rectangle’s area. use the following formula: area = length * width if the user enters 3, the program should ask for the length of the triangle’s base and its height, and then display its area. use the following formula: area = base * height * .5 if the user enters 4, the program should end. input validation: display an error message if the user enters a number outside the range of 1 through 4 when selecting an item from the menu. do not accept negative values for the circle’s radius, the rectangle’s length or width, or the triangle’s base or height. note: if the user enters an improper menu choice (1-4), the program prints "the valid choices are 1 through 4. run the program again and select one of those." if the user enters a negative radius, the program prints "the radius can not be less than zero." if the user enters a negative value for height or base, the program prints "only enter positive values for base and height."