// This is an application file, which uses functionality of// the Complex class to implement new functionality#include <iostream>#include <cmath>// This is needed to use Complex objects#include "complex.h"// Declarations of functions defined in this fileComplex exp( Complex z );Complex pow( Complex z, double x );Complex sqrt( Complex z );using namespace std;int main(){	// ipi = 0 + i*pi, where pi = 3.14159...	Complex ipi(0, M_PI);	// e^(i*pi) = -1	cout << "exp(i*pi)=" << exp(ipi) << endl;		// z = i, the imaginary unit	Complex z(0.0, 1.0);	// Print out the value of z	cout << "z=" << z << endl;	// Compute the square root of i, which is	// sqrt(2)/2 + sqrt(2)/2 i	cout << "sqrt(z)=" << sqrt(z) << endl;		// A complex number z has n nth roots, which lie on	// the circle in the complex plane of radius r^(1/n), 	// where r = |z|.  These roots can be found by noting	// that if 	//	// z = r*exp(i*t) = r*(cos(t) + i*sin(t)), 	//	// where (r,t) are the polar coordinates of z, then	//	// z1 = r^(1/n)*(cos(t/n)+i*sin(t/n))	//	// is an nth root of z, and so are z1*exp(2pi*i*j/n), 	// for j=1,...,n-1. Here we compute the four 4th roots 	// of z=i.	int n = 4;	// pow(z,1/n) computes z1 above	Complex z1( pow(z, 1.0 / n) );	// rootj = z1*e^(2pi*i*j/n), for j=0,1,...,n-1	Complex rootj(z1);	// shift = 2pi*i/n simplifies computation of rootj	Complex shift(0, 2.0*M_PI/n);	for ( int j = 0; j < n; j++ )	{		// Now output z1*e^(2pi*i*j/n), for j=0,1,...,n-1		cout << "root " << j+1 << "=" << rootj << endl;		rootj *= exp(shift);	}	return 0;}Complex exp( Complex z ){	// z = u + iv => exp(z) = exp(u)(cos(v) + i cos(v))	Complex y(cos(z.Im()), sin(z.Im()));	y *= std::exp(z.Re());	return y;}Complex pow( Complex z, double x ){	// z = r*exp(it) => z^x = r^x*exp(itx)	double arg = z.Arg();	if ( arg == 0.0 )		arg = arg + 2.0 * M_PI;	Complex y(cos(arg*x), sin(arg*x));	y *= std::pow(z.Abs(), x);	return y;}Complex sqrt( Complex z ){	// Just use pow with exponent 1/2	return pow( z, 0.5 );}