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/*C++ program to multiply two complex numbers using * operator overloading*/ #include<iostream.h> #include<conio.h> class complex { float x,y; public: complex() {} complex(float real,float img) { x=real; y=img; } complex operator*(complex); void display() { cout<<x<<" + "<<y<<"i"<<endl; } }; complex complex::operator*(complex e) { complex temp; temp.x=x*e.x+y*e.y*(-1); temp.y=x*e.y+y*e.x; return(temp); } void main() { clrscr(); complex c1(5,3),c2(3,2),c3=c1*c2; c1.display(); c2.display(); cout<<"Multiplication"<<endl; c3.display(); getch(); } OUTPUT: 5 + 3i 3 + 2i Multiplication 9 + 19i
A complex number is a combination of real and imaginary numbers. An example of a complex number is the expression (a + jb), in which the letter j is called an 'operator'. In this example, the operator +j indicates that the quantity b is acting at an angle of +90o to quantity a -or is 'leading' a by 90o. If the operator was -j, then it would be indicating that quantity bis acting at -90o to quantity a -or is 'lagging' a by 90o.Mathematicians use the letter 'i' to represent an imaginary number, but in electrical engineering we use the letter 'j'. This is because we already use a lower-case 'i'to represent an instantaneous value of current. In mathematics, the operator is sometimes written after the quantity to which it applies (i.e. 'bj'), but it is more usual, in engineering, to place the operator in front of that quantity (i.e. 'jb').The application of the operator 'j' to a phasor, then, acts to rotate that phasor, counterclockwise, through 90 degrees.The term, 'imaginary', is misleading -it doesn't mean that it exists only in the mind! It is simply a mathematician's term for 'quadrature', meaning 'lying along the y-axis'.A.C. quantities, such as current and voltage, can be resolved into horizontal and vertical components. So, we can represent an alternating-current quantity by a complex number which represents its in-phase component together with its quadrature (plus or minus 90o) component. For example, 3+j4 could represent a 5-A current, whose in-phase component is 3 A, and whose quadrature component is 4 A (i.e. which leads the in-phase component by 90o).Complex numbers enable complex a.c. circuits to be resolved relatively easily, and without the need to construct complicated phasor diagrams.As in-phase and quadrature ('imaginary') components only apply to a.c. quantities, we do not need to apply complex numbers to d.c.
An Assignment operator in Java is the operator that is used to assign a variable a value. if you declare int x = 10; then the value 10 is assigned to the variable x. here the "=" symbol is the assignment operator.
The prefix increment operator is overloaded as operator++() while the postfix increment operator is overloaded as operator++(int).
A
Adjoint operator of a complex number?
The hamiltonian operator is the observable corresponding to the total energy of the system. As with all observables it is given by a hermitian or self adjoint operator. This is true whether the hamiltonian is limited to momentum or contains potential.
relationship between determinant and adjoint
You cannot create a new operator through operator overloading. You can only redefine an existing operator, with certain limitations. As an example, for a class of complex numbers, having a real and an imaginary part, you might want an addition operator. This is the skeleton of code to do that. I only show the operator, not any constructors or other operators or methods, etc.class complex {private:double real, imaginary;public:complex operator+ (complex operand) {complex temp;temp.real = this.real + operand.real;temp.imaginary = this.imaginary + operand.imaginary;return temp;}};The above answer is for C++. Since this question is also categorized in Java Programming it's important to note that operator overloading is not currently possible in Java.
The classical adjoint of a square matrix A the transpose of the matrix who (i, j) entry is the a i j cofactor.
/*C++ program to multiply two complex numbers using * operator overloading*/ #include<iostream.h> #include<conio.h> class complex { float x,y; public: complex() {} complex(float real,float img) { x=real; y=img; } complex operator*(complex); void display() { cout<<x<<" + "<<y<<"i"<<endl; } }; complex complex::operator*(complex e) { complex temp; temp.x=x*e.x+y*e.y*(-1); temp.y=x*e.y+y*e.x; return(temp); } void main() { clrscr(); complex c1(5,3),c2(3,2),c3=c1*c2; c1.display(); c2.display(); cout<<"Multiplication"<<endl; c3.display(); getch(); } OUTPUT: 5 + 3i 3 + 2i Multiplication 9 + 19i
adjugatee matrix
A complex formula in Excel could have many arithmetic operators in it. There are many things that make a formula complex, so a formula with just one arithmetic operator or even no arithmentic operators could be complex too, depending on what it does.
#include<iostream.h> #include<conio.h> class complex { int r; int i; public: complex() { } complex(int a,int b) { r=a;i=b; } friend complex operator+(complex,complex); friend show(complex); complex operator+(complex c1,complex c2) { complex c3; c3.r=c1.r+c2.r; c3.i=c1.i+c2.i; return(c3); } show(complex c) { cout<<c.r<<"i+"<<c.i<<endl; } void main() { complex a,b,c; clrscr(); a.complex(3,6); b.complex(4,7); c=a+b; show(a); show(b); show(c); getch() }
An adjoint is a matrix in which each element is the cofactor of an associated element of another matrix.
Since you didn't show an operator, we'll use: 1. 8-6i 2. 8+6i 3. 8 times 6i = 48i The complex conjugates are: 1. 8+6i 2. 8-6i 3. -48i
consider the following second order diffenential x d2y/dx2+(1-x)dy/dx+ny=0 is this equation self adjoint if not self adjoint equation find p(x)and the weight funtion s(x)