Homework #9

• Goal: Learn to use the square root and cosine functions in the mathematical library.
• Please UPLOAD your homework (ZIP or RAR file) to TA at http://ms11.voip.edu.tw/cs102/
• Deadline: 2008/4/19 11:00 AM
• Background:
  1. In Visual C++, sqrt() is a function in Math class which returns the square root of a specified number, while the cos() function takes an angle and returns the ratio of two sides of a right triangle. The ratio is the length of the side adjacent to the angle divided by the length of the hypotenuse.
  2. M_PI is a constant with the value pi, while M_PI_2 is a constant with the value pi/2.
  3. Be sure to include <math.h> in your C++ program to access these functions and constants.
  4. Also see the file VisualStudio8\VC\include\math.h for other popular constants.
  5. To use these math constants, you have to define _USE_MATH_DEFINES before the #including math.h.
• Let w = cos(2*pi/n) + i sin(2*pi/n). Write a program to take the input n, and print out the complex number w, and the result of 1 + w + w^2 + w^3 + ... + w^(n-1).
• Note: Overload the operator^ to be the integer power over a complex number, i.e., w^3 = w * w * w. In this exercise, you may assume the integer power to be non-negative.