//////////////////////////////////////////////////// /// /// Complex Numbers in C++ /// /////////////////////////////////////////////////////// /// Made By - Kinshuk Vasisht /// Version - 2.1.1 /// Status - 0xFFFFEE (Complete, add-ons /// possible...) /// Features - Complex Number Operations /// Radian - Degree Conversion, /// Overloads - Templates & Declarations... /// Functions - radtodeg(), degtorad(), /// Signum(), /// Complex Class Methods /// Main Data Type - Long Double (as Alias - ld) /// Templates - typename Only. /// Macros - None. /// Classes - Complex(Operator,Function) /// * Complex Features - /// # Functions - Get(),Print(),Re(),Im(), /// Root(),RaiseToComplex(), /// Log(),Modulus(),Argument(), /// Normal(),Conjugate(), /// GetPolar(),Print1Polar(), /// Print2Polar(),Inverse(), /// Polar(),Rotate(),Sin(), /// Cos(),Tan(),Sinh(),Cosh(), /// Tanh(),Exponent()... /// # Operators - +,-,*,/,*2,+=,-=,*=,/=, /// ==,!=,^,^,>,<,~,-,<<, /// #defines - Pi (Pi), Eu (Euler's Number) /// No. of Lines - 490 (No Extras) /// Headers - , , /// , /// Contributions - Thanks to JPM for his /// Contributions to some of the /// Complex Class' Math... /// - Modification Inspired by /// JPM's Program - /// - https://code.sololearn.com/ /// ci2z3XExdMcE/#cpp /// - Only Signum Modification, /// Root Overload(nth Root), /// Friend Operators and bool /// Operators are inspired... /// //////////////////////////////////////////////////// /* Hello. 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 a simple program 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... */ #include #include #include #include #define Pi 3.141592653589793 #define Eu 2.718281828459045 typedef long double ld; typedef long long int l; using namespace std; int signum(ld x) { return (0>arg; cout<<"Enter the Modulus - ";cin>>mod; cout<0) 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; } void Rotate(ld angle) ///Rotates the Complex Number by 'angle' Degrees { ld a=Modulus(),b=Argument(); b+=angle; ld bx=degtorad(b); real=a*cos(bx); imag=a*sin(bx); } void RaiseToComplex(ld a,Complex& z) ///Returns a raised to 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; } Complex Cos() ///Returns Cosine of Complex z { 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(2.718281828459045,t3); t6.RaiseToComplex(2.718281828459045,t4); t7=t5+t6; res.real=t7.real/2; res.imag=t7.imag/2; return res; } Complex Cosh() ///Returns Hyperbolic Cosine of Complex z { Complex res,t1(real,imag),t2(-real,-imag),t3,t4,t5; t3.RaiseToComplex(2.718281828459045,t1); t4.RaiseToComplex(2.718281828459045,t2); t5=t4+t3; res.real=t5.real/2; res.imag=t5.imag/2; return res; } Complex Sin() ///Returns Sine of Complex z { 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(2.718281828459045,t3); t6.RaiseToComplex(2.718281828459045,t4); t7=t6-t5; t8=t7*t; res.real=t8.real/2; res.imag=t8.imag/2; return res; } Complex Sinh() ///Returns Hyperbolic Sine of Complex z { Complex res,t1(real,imag),t2(-real,-imag),t3,t4,t5; t3.RaiseToComplex(2.718281828459045,t1); t4.RaiseToComplex(2.718281828459045,t2); t5=t3-t4; res.real=t5.real/2; res.imag=t5.imag/2; return res; } Complex Tan() ///Returns Tangent of Complex z { Complex res,t1,t2; t1=Sin(); t2=Cos(); res=t1/t2; return res; } Complex Tanh() ///Returns Hyperbolic Tangent of Complex z { Complex res,t1,t2; t1=Sinh(); t2=Cosh(); res=t1/t2; return res; } Complex Exp() { Complex res; res.RaiseToComplex(Eu,*this); return res; } Complex Log(ld base) ///Returns Log of the Complex No. to the base { Complex res; res.real=log(Modulus())/((log(base))); res.imag=degtorad(Argument())/((log(base))); return res; } bool operator==(const Complex& rhs) ///Checks if the Complex Numbers are Equal { return(real==rhs.real&&imag==rhs.imag); } bool operator!=(const Complex& rhs) //Checks if the Complex Numbers are Unequal { return(real!=rhs.real&&imag!=rhs.imag); } Complex operator~() ///Returns Conjugate of the Complex Number { *this=Conjugate(); return *this; } Complex operator+(Complex rhs) ///Adds Two Complex Numbers { Complex res; res.real=real+rhs.real; res.imag=imag+rhs.imag; return res; } Complex operator+(ld rhs) ///Adds Constant to Complex Number { Complex res; res.real=real+rhs; res.imag=imag; return res; } Complex operator-(Complex rhs) ///Subtracts Two Complex Numbers { Complex res; res.real=real-rhs.real; res.imag=imag-rhs.imag; return res; } Complex operator-(ld rhs) ///Subtracts Constant from Complex Number { Complex res; res.real=real-rhs; res.imag=imag; return res; } Complex operator*(Complex rhs) ///Multiplies Two Complex Numbers { Complex res; res.real=(real*rhs.real)-(imag*rhs.imag); res.imag=(real*rhs.imag)+(imag*rhs.real); return res; } Complex operator*(ld rhs) ///Multiplies Complex z by a Constant { Complex res; res.real=real*rhs; res.imag=imag*rhs; return res; } Complex operator/(Complex rhs) ///Divides Two Complex Numbers { rhs.Inverse(); Complex res; res.real=(real*rhs.real)-(imag*rhs.imag); res.imag=(real*rhs.imag)+(imag*rhs.real); return res; } Complex operator/(ld rhs) ///Divides Complex z by a Constant { Complex res; res.real=real/rhs; res.imag=imag/rhs; return res; } void operator+=(Complex rhs) ///Adds z2 to z1 { real+=rhs.real; imag+=rhs.imag; } void operator-=(Complex rhs) ///Subtracts z2 from z1 { real-=rhs.real; imag-=rhs.imag; } void operator*=(Complex rhs) ///Multiplies z2 and z1 and returns to z1 { real=(real*rhs.real)-(imag*rhs.imag); imag=(real*rhs.imag)+(imag*rhs.real); } void operator/=(Complex rhs) ///Divides z2 and z1 and returns to z1 { rhs.Inverse(); real=(real*rhs.real)-(imag*rhs.imag); imag=(real*rhs.imag)+(imag*rhs.real); } void operator+=(ld rhs) ///Adds Constant to z1 { real+=rhs; imag=imag; } void operator-=(ld rhs) ///Subtracts Constant from z1 { real-=rhs; imag=imag; } void operator*=(ld rhs) ///Multiplies z1 with a Constant and returns to z1 { real*=rhs; imag*=rhs; } void operator/=(ld rhs) ///Divides z1 with a Constant and returns to z1 { real/=rhs; imag/=rhs; } Complex operator^(ld power) ///Returns Complex z Raised to '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; } Complex operator^(Complex b) ///Returns Complex z1 raised to Complex z2 { 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; } ~Complex(){} ///Complex Destructor -- Does Nothing till now... ///Non - Member friend Overloads... friend Complex operator+(ld rhs,Complex c) { return(Complex(c.real+rhs,c.imag)); } friend Complex operator-(ld rhs,Complex c) { return(Complex(c.real-rhs,c.imag)); } friend Complex operator*(ld rhs,Complex c) { return(Complex(c.real*rhs,c.imag*rhs)); } friend Complex operator/(ld rhs,Complex c) { return(Complex(c.real/rhs,c.imag/rhs)); } friend Complex operator^(ld rhs,Complex c) { Complex res; ld t1,t2,t3; t1=pow(rhs,c.real); t2=cos(c.imag*log(rhs)); t3=sin(c.imag*log(rhs)); res.real=t1*t2; res.imag=t1*t3; return res; } }; /* Example Program 1 - Returns Orthocentre of 3 Complex Numbers z1, z2 and z3... Complex z1,z2,z3,t1,t2,t3,r1,r2,r3,res; ld a1,a2,a3; z1.Get(); z2.Get(); z3.Get(); t1=z1.Conjugate(); t2=z2.Conjugate(); t3=z3.Conjugate(); a1=z1.Normal(); a2=z2.Normal(); a3=z3.Normal(); r1=((z1^2)*(t2-t3))+((z2^2)*(t3-t1))+((z3^2)*(t1-t2)); r2=((z2-z3)*a1)+((z3-z1)*a2)+((z1-z2)*a3); r3=(z1*t2)-(z2*t1)+(z2*t3)-(z3*t2)+(z3*t1)-(z1*t3); res=(r1+r2)/r3; cout<<"Orthocentre - "<>no; cout<

Complex Numbers in C++ - Tab Version