library complex_numbers;

import 'dart:math' as math;

class ComplexNumber {
  num _real;
  num _imag;

// 1- Here we define different ways to build a complex number:
  // constructors:
     ComplexNumber([this._real = 0, this._imag = 0]);
    ComplexNumber.im(num imag) : this(0, imag);
     ComplexNumber.re(num real) : this(real, 0);

// 2- The normal utility methods to get and set the real and         // imaginary part, to get the absolute value and the angle, to      // compare two complex numbers:
  num get real => _real;
  set real(num value) => _real = value;

  num get imag => _imag;
  set imag(num value) => _imag = value;

  num get abs => math.sqrt(real * real + imag * imag);

  num get angle => math.atan2(imag, real);

  bool operator ==(other) {
    if (!(other is ComplexNumber)) {
      return false;
    }
    return this.real == other.real && this.imag == other.imag;
  }

  String toString() {
    if (_imag >= 0) {
      return '${_real} + ${_imag}i';
    }
    return '${_real} - ${_imag.abs()}i';
  }
// 3- operator overloading:
// The basic operations for adding, multiplying, subtraction and    // division are defined as overloading of the operators +, *, - and / 
  ComplexNumber operator +(ComplexNumber x) {
    return new ComplexNumber(_real + x.real, _imag + x.imag);
  }

  ComplexNumber operator -(var x) {
    if (x is ComplexNumber) {
return new ComplexNumber(this.real - x.real, this.imag - x.imag);
    } else if (x is num) {
      _real -= x;
      return this;
    }
    throw 'Not a number';
  }

  ComplexNumber operator *(var x) {
    if (x is ComplexNumber) {
      num realAux = (this.real * x.real - this.imag * x.imag);
      num imagAux = (this.imag * x.real + this.real * x.imag);

      return new ComplexNumber(realAux, imagAux);
    } else if (x is num) {
      return new ComplexNumber(this.real * x, this.imag * x);
    }
    throw 'Not a number';
  }

  ComplexNumber operator /(var x) {
    if (x is ComplexNumber) {
num realAux = (this.real * x.real + this.imag * x.imag) / (x.real * x.real + x.imag * x.imag);
num imagAux = (this.imag * x.real - this.real * x.imag) / (x.real * x.real + x.imag * x.imag);
      return new ComplexNumber(realAux, imagAux);
    } else if (x is num) {
      return new ComplexNumber(this.real / x, this.imag / x);
    }
    throw 'Not a number';
  }

// 4- Here we define the same operations as methods:
 static ComplexNumber add(ComplexNumber c1, ComplexNumber c2)     {
    num rr = c1.real + c2.real;
    num ii = c1.imag + c2.imag;
    return new ComplexNumber(rr, ii);
 }

 static ComplexNumber subtract(ComplexNumber c1, ComplexNumber c2) 
 {
    num rr = c1.real - c2.real;
    num ii = c1.imag - c2.imag;
    return new ComplexNumber(rr, ii);
 }

 static ComplexNumber multiply(ComplexNumber c1, ComplexNumber c2) 
 {
    num rr = c1.real * c2.real - c1.imag * c2.imag;
    num ii = c1.real * c2.imag + c1.imag * c2.real;
    return new ComplexNumber(rr, ii);
 }

 static ComplexNumber divide(ComplexNumber c1, ComplexNumber c2) 
 {
num real = (c1.real * c2.real + c1.imag * c2.imag) / (c2.real * c2.real + c2.imag * c2.imag);
num imag = (c1.imag * c2.real - c1.real * c2.imag) /  (c2.real * c2.real + c2.imag * c2.imag);
    return new ComplexNumber(real, imag);
 }
}