//=========================================================================
#define PROGRAMMER "SOLUTIONS, Nofrills"
#define PROG_CODE  "soln"
#define COURSE     "ECE-1021"
#define YEAR       (2004)
#define TERM       "Spring"
#define SECTION    (0)
#define ASSIGNMENT "HW #8A"
#define REVISION   (0)
#define TITLE      "Complex Math"
#define SUBTITLE   "Last Modified on 23 APR 04"
#define EMAIL      "ece1021@eas.uccs.edu"
#define FILENAME   "08a0soln.c"
//=========================================================================

//=========================================================================
// PROBLEM
//=========================================================================
//
// Programming Problem #10.3
//
// Implement primitive functions and utility functions before implementing
// the functions called for in the problem.
//
//=========================================================================
// PSEUDOCODE
//=========================================================================
//
// This is a set of very specific functions and so no detailed pseudocode
// is really appropriate. But a description of each function is warranted.
//
// Structure:
//
// struct complex
// {
//    double real, imaginary;
// };
// typedef struct complex COMPLEX;
//
// Primitive Functions:
//
// double GetCOMPLEXreal(COMPLEX a);
// double GetCOMPLEXimag(COMPLEX a);
// double SetCOMPLEXreal(COMPLEX *a, double real);  //returns real
// double SetCOMPLEXimag(COMPLEX *a, double imag);  //returns imag
//
// Utility Functions:
//
// The following can use the Primitives directly:
//
// Re(a): returns the real part of the complex number a
// Im(a): returns the imaginary part of the complex number a
// cartesian(real, imaginary): returns a complex number
//
// The following need to perform polar to rectangular conversions:
//
// Mag(a): returns the magnitude of the complex number a
//         |c| = sqrt( (Re(c))^2 + (Im(c))^2 )
// Arg(a): returns the arg (the angle in radians) of the complex number a
//         arg = atans(Im(c), Re(c))
// polar(magnitude, arg): returns a complex number
//         Re(c) = magnitude*cos(arg), Im(c) = magnitude*sin(arg)
//
// Functions:
// add_c(a,b)    return a + b
//               Re(c) = Re(a) + Re(b), Im(c) = Im(a) + Im(b)
//
// sub_c(a,b)    return a - b
//               Re(c) = Re(a) - Re(b), Im(c) = Im(a) - Im(b)
//
// mul_c(a,b)    return a * b
//               Re(c) = Re(a)Re(b) - Im(a)Im(b)
//               Im(c) = Re(a)Im(b) + Im(a)Re(b)
//                 Or, using the polar functions:
//               c = Polar( Mag(a)*Mag(b), Arg(a)+Arg(b) )
//
// div_c(a,b)    return a / b
//               c = Polar( Mag(a)/Mag(b), Arg(a)-Arg(b) )
//
// read_c(ptr2c) read a complex number from the keyboard and store in c
//               Have user type in using the form 7+5i (no spaces)
//
// print_c(a)    print out the complex number a
//               Output in the form " Re(a)+Im(a)i "
//
// conj_c(a)     returns complex conjugate
//               c = cartesian( Re(a), -Im(a) )
//
// abs_c(a)      returns magnitude of a (result is double)
//               m = Mag(a)
//
// exp_c(a)      returns exp(a) (result is complex)
//               c = cartesian(exp(Re(a))cos(Im(a)), exp(Re(a))sin(Im(a)))
}