/// INPUT - Nothing. Its just Code /// Playground responding to /// uncalled cin functions. /// OUTPUT - See for Yourself... ^_^ /* The following is a simpler implementation of complex numbers in C++; Numbers of the form a + b i, where a and b are real and i = sqrt(-1). This class declaration allows the user to perform most of the possible operations as possible using complex numbers... The equations can be of any difficulty, as most of the functions are here. All depends on the user's imagination and knowledge of implementation... Also , I have left simple programs after the class declaration to demonstate how to use this class for calculations... If you have any queries or suggestions, please let me know in the comments... /// WHATS NEW - I have added format flags and manipulators! Now one can print in multiple ways with cout. */ #include #include #include #include #include #include #include #define Pi 3.141592653589793 #define Eu 2.718281828459045 typedef double ld; #define fmt ios_base::fmtflags typedef long long int l; using namespace std; bool polar_cossin_type = false, polar_e_type = false, iota_type = false, general = true , i_polar_cossin = false, i_polar_e = false, i_iota = false, i_general = false; ostream& iota (ostream& os); ostream& polar_e (ostream& os); ostream& polar_cs(ostream& os); ostream& normal (ostream& os); istream& iota (istream& is); istream& polar_e (istream& is); istream& polar_cs(istream& is); istream& normal (istream& is); int signum (ld x); ld degtorad (ld deg); ld radtodeg (ld rad); class Complex { private: ld real; ld imag; public: static const ios_base::fmtflags polar_cs = static_cast(0x4000), polar_e = static_cast(0x2000), iota = static_cast(0x1000); ///Complex Constructor. Complex(ld re=0,ld im=0): real(re),imag(im){} ///Complex Copy Constructor Complex(const Complex& c2): real(c2.real),imag(c2.imag){} ///Gets the Real and Imaginary Parts. void Get() { cout<<"Enter Real Value = "; cin>>real; cout<<"Enter Imaginary Value = "; cin>>imag; cout<0) { cout<<"The Number is = "<>arg; cout<<"Enter the Modulus - "; cin>>mod; cout< Root() { ld a=Modulus(); Complex x1, x2; x1.real=sqrt((a+real)/2); x1.imag=signum(imag)* sqrt((-real+a)/2); x2.real=-(sqrt((a+real)/2)); x2.imag=-(signum(imag)* sqrt((-real+a)/2)); return make_pair(x1,x2); } ///Returns nth Roots of z as a vector vector Root(int m) { int n=abs(m); vector z; ld rn=pow(Modulus(),1.0/n); ld narg=(degtorad(Argument()))/n; ld npi=(2.0*Pi)/n; for(int i=0;i0) z[k]=Complex(rn*cos(narg+k*npi), rn*sin(narg+k*npi)); else z[k]=Complex(rn*cos(narg+(-k)*npi), rn*sin(narg+(-k)*npi)); } return z; } ///Rotates the Number by 'angle' Degrees void Rotate(ld angle) { ld a=Modulus(),b=Argument(); b+=angle; ld bx=degtorad(b); real=a*cos(bx); imag=a*sin(bx); } ///Returns a raised to Complex z void RaiseToComplex(ld a,Complex z) { cout.precision(8); cout.setf(ios::fixed); ld t1,t2,t3; t1=pow(a,z.real); t2=cos(z.imag*log(a)); t3=sin(z.imag*log(a)); real=t1*t2; imag=t1*t3; } ///Returns Cosine of Complex z Complex Cos() const { Complex res,t1(0,1),t2(0,-1), t3,t4,t5,t6,t7; t3.real=(real*t1.real)- (imag*t1.imag); t3.imag=(real*t1.imag)+ (imag*t1.real); t4.real=(real*t2.real)- (imag*t2.imag); t4.imag=(real*t2.imag)+ (imag*t2.real); t5.RaiseToComplex(Eu,t3); t6.RaiseToComplex(Eu,t4); t7=t5+t6; res.real=t7.real/2; res.imag=t7.imag/2; return res; } ///Returns Hyperbolic Cosine of z Complex Cosh() const { Complex res,t1(real,imag), t2(-real,-imag),t3,t4,t5; t3.RaiseToComplex(Eu,t1); t4.RaiseToComplex(Eu,t2); t5=t4+t3; res.real=t5.real/2; res.imag=t5.imag/2; return res; } ///Returns Sine of Complex z Complex Sin() const { Complex res,t(0,1),t1(0,1),t2(0,-1), t3,t4,t5,t6,t7,t8; t3.real=(real*t1.real)- (imag*t1.imag); t3.imag=(real*t1.imag)+ (imag*t1.real); t4.real=(real*t2.real)- (imag*t2.imag); t4.imag=(real*t2.imag)+ (imag*t2.real); t5.RaiseToComplex(Eu,t3); t6.RaiseToComplex(Eu,t4); t7=t6-t5; t8=t7*t; res.real=t8.real/2; res.imag=t8.imag/2; return res; } ///Returns Hyperbolic Sine of z Complex Sinh() const { Complex res,t1(real,imag), t2(-real,-imag),t3,t4,t5; t3.RaiseToComplex(Eu,t1); t4.RaiseToComplex(Eu,t2); t5=t3-t4; res.real=t5.real/2; res.imag=t5.imag/2; return res; } ///Returns Tangent of Complex z Complex Tan() const { Complex res,t1,t2; t1=Sin(); t2=Cos(); res=t1/t2; return res; } ///Returns Hyperbolic Tangent of z Complex Tanh() const { Complex res,t1,t2; t1=Sinh(); t2=Cosh(); res=t1/t2; return res; } /// Returns e^z for Complex z Complex Exp() const { Complex res; res.RaiseToComplex(Eu,*this); return res; } ///Returns Log of z to the base Complex Log(ld base) const { Complex res; res.real=log(Modulus())/ ((log(base))); res.imag=degtorad(Argument())/ ((log(base))); return res; } ///Checks if the Numbers are Equal bool operator==(const Complex& rhs) { return(real==rhs.real&& imag==rhs.imag); } ///Checks if the Numbers are Unequal bool operator!=(const Complex& rhs) { return(real!=rhs.real&& imag!=rhs.imag); } ///Returns Conjugate of the Number Complex operator~() { Complex res=Conjugate(); return res; } ///Adds Two Complex Numbers Complex operator+(Complex rhs) { Complex res; res.real=real+rhs.real; res.imag=imag+rhs.imag; return res; } ///Adds Constant to Complex Number Complex operator+(ld rhs) { Complex res; res.real=real+rhs; res.imag=imag; return res; } ///Subtracts Two Complex Numbers Complex operator-(Complex rhs) { Complex res; res.real=real-rhs.real; res.imag=imag-rhs.imag; return res; } ///Subtracts Constant from Complex Number Complex operator-(ld rhs) { Complex res; res.real=real-rhs; res.imag=imag; return res; } ///Multiplies Two Complex Numbers Complex operator*(Complex rhs) { Complex res; res.real=(real*rhs.real)- (imag*rhs.imag); res.imag=(real*rhs.imag)+ (imag*rhs.real); return res; } ///Multiplies Complex z by a Constant Complex operator*(ld rhs) { Complex res; res.real=real*rhs; res.imag=imag*rhs; return res; } ///Divides Two Complex Numbers Complex operator/(Complex rhs) { rhs.Inverse(); Complex res; res.real=(real*rhs.real)- (imag*rhs.imag); res.imag=(real*rhs.imag)+ (imag*rhs.real); return res; } ///Divides Complex z by a Constant Complex operator/(ld rhs) { Complex res; res.real=real/rhs; res.imag=imag/rhs; return res; } ///Adds z2 to z1, Assignment void operator+=(Complex rhs) { real+=rhs.real; imag+=rhs.imag; } ///Subtracts z2 from z1, Assignment void operator-=(Complex rhs) { real-=rhs.real; imag-=rhs.imag; } ///Multiplies z1 by z2, Assignment void operator*=(Complex rhs) { real=(real*rhs.real)-(imag*rhs.imag); imag=(real*rhs.imag)+(imag*rhs.real); } ///Divides z1 by z2, Assignment void operator/=(Complex rhs) { rhs.Inverse(); real=(real*rhs.real)-(imag*rhs.imag); imag=(real*rhs.imag)+(imag*rhs.real); } ///Adds Constant to z1 void operator+=(ld rhs) { real+=rhs; imag=imag; } ///Subtracts Constant from z1 void operator-=(ld rhs) { real-=rhs; imag=imag; } ///Multiplies z1 with a Constant void operator*=(ld rhs) { real*=rhs; imag*=rhs; } ///Divides z1 with a Constant void operator/=(ld rhs) { real/=rhs; imag/=rhs; } ///Returns Complex z Raised to 'power' Complex operator^(ld power) { ld a,b; a=Modulus(); b=pow(a,power); ld c,d; d=Argument(); c=degtorad(d); Complex res; res.real=b*cos(power*c); res.imag=b*sin(power*c); return res; } ///Returns z1 raised to Complex z2 Complex operator^(Complex b) { Complex res,t1(0,1), t2(b.real/2,b.imag/2),t3,t4,t5,t6; ld a1,a2; a1=Normal();a2=degtorad(Argument()); t3.RaiseToComplex(a1,t2); t4=t1*b; t5.real=t4.real*a2; t5.imag=t4.imag*a2; t6.RaiseToComplex(Eu,t5); res=t6*t3; return res; } ///Raises z1 by z2, Assignment void operator^=(Complex z2) { *this = *this^z2; } /// Raises z by Constant and Saves to z void operator^=(ld rhs) { *this = *this^rhs; } ///Complex Destructor ~Complex(){} /// Adds Constant to Complex Number friend Complex operator+(ld rs,Complex c) { return(Complex(c.real+rs,c.imag)); } /// Subtracts Constant from Number friend Complex operator-(ld rs,Complex c) { return(Complex(c.real-rs,c.imag)); } /// Multiplies Constant with z friend Complex operator*(ld rs,Complex c) { return(Complex(c.real*rs,c.imag*rs)); } /// Divides Complex Number by Constant friend Complex operator/(ld rs,Complex c) { return(Complex(c.real/rs,c.imag/rs)); } /// Raises Constant to the Power of z friend Complex operator^(ld rs,Complex c) { Complex res; ld t1,t2,t3; t1=pow(rs,c.real); t2=cos(c.imag*log(rs)); t3=sin(c.imag*log(rs)); res.real=t1*t2; res.imag=t1*t3; return res; } // Prints The Complex Number friend ostream& operator<< (ostream& os, Complex c) { os.setf(ios::fixed); os.precision(3); if(((os.flags()&iota)== 0x1000)||iota_type==true) { os<0?"+":"-")<< " "<> (istream& is,Complex& c) { if(((is.flags()&iota)== 0x1000)||i_iota==true) { is>>c.real; string s,res; getline(is,s); bool sign=0, rs=0, rd=false; for(char c:s) { if(c=='-'&&rs!=true) {sign=true; rs=true;} else if(c=='+'&&rs!=true) {rs=true;} else if(rd!=true&&c=='.') {res+='.'; rd=true;} else if(c=='i'||c=='j') break; else if(isdigit(c)) res+=c; else continue; } res = ((sign==true)? ("-"+res):(res)); c.imag = strtof(res.c_str(),0LL); } else if(((is.flags()&polar_e) ==0x2000)||polar_e_type==true) { ld mod, arg; string s,res[2]; getline(is,s); int i=0; bool sign[2]={0,0}, rs[2]={0,0}, rd[2]={0,0}; for(char c:s) { if(c=='-'&&rs[i]!=true) {sign[i]=true; rs[i]=true;} else if(c=='+'&&rs[i]!=true) {rs[i]=true;} else if(rd[i]!=true&&c=='.') {res[i]+='.'; rd[i]=true;} else if(c=='*') i++; else if(c==')') break; else if(isdigit(c)) res[i]+=c; else continue; } res[0] = ((sign[0]==true)? ("-"+res[0]):(res[0])); res[1] = ((sign[1]==true)? ("-"+res[1]):(res[1])); mod = strtof(res[0].c_str(),0LL); arg = strtof(res[1].c_str(),0LL); c.Polar(mod,radtodeg(arg)); } else if(((is.flags()&polar_cs)== 0x4000)||i_polar_cossin==true) { ld mod, arg; string s,res[2]; getline(is,s); int i=0; bool sign[2]={0,0}, rs[2]={0,0}, rd[2]={0,0}; for(char c:s) { if(c=='-'&&rs[i]!=true) {sign[i]=true; rs[i]=true;} else if(c=='+'&&rs[i]!=true) {rs[i]=true;} else if(rd[i]!=true&&c=='.') {res[i]+='.'; rd[i]=true;} else if(c=='*') i++; else if(c==')') break; else if(isdigit(c)) res[i]+=c; else continue; } res[0] = ((sign[0]==true)? ("-"+res[0]):(res[0])); res[1] = ((sign[1]==true)? ("-"+res[1]):(res[1])); mod = strtof(res[0].c_str(),0LL); arg = strtof(res[1].c_str(),0LL); c.Polar(mod,arg); } else { is>>c.real>>c.imag; } return is; } }; inline void __RESET__(ostream& os) /// Function to Reset Format Flags { os.unsetf(Complex::iota); os.unsetf(Complex::polar_e); os.unsetf(Complex::polar_cs); polar_cossin_type = false; polar_e_type=false; iota_type=false; } inline void __RESET__(istream& is) { is.unsetf(Complex::iota); is.unsetf(Complex::polar_e); is.unsetf(Complex::polar_cs); i_polar_cossin = false; i_polar_e=false; i_iota=false; } /* Example Program 1 - Returns n'th roots of a Complex Number in an Array... Complex z1,sum; vector z2; z1.Get(); ld no; cout<<"Enter 'n' in nth Root - "; cin>>no; cout<>iota>>c; cout<<"C = "<>polar_cs>>c; cout<<"C = "< p1 = c1.Root(); cout<<"c1+c2 = "<

Complex Numbers in C++ - A Better Approach...