if a is real its eigen values are real or complex conjugates in pairs.

If x and y are real numbers, then x + iy is called a complex number. x is called the real part and y is called the imaginary part. The complex number x + iy is also written as an ordered pair (x, y) and is denoted by z. i.e., z = x + iy The positive..

Square root of a negative number is known as an imaginary number . If x and y are real numbers, then x + iy is called a complex number . x is called the real part and y is called the imaginary part . The following are the types of complex..

Optics..

Real Function: A real valued function f : A to B or simply a real function 'f ' is a rule which associates to each possible real number x A, a unique real number f(x) B, when A and B are subsets of R, the set of real numb..

Geometrical representation of a Complex number, Argand diagram - Since every complex number z = x + iy is an order pair of real numbers (x, y), it can therefore be represented by a point P(x,y) in the xy plane by taking the real part along the x-axi..

Graphical representation of Complex numbers - The complex number Z = x + iy may be represented graphically by the point P whose rectangular co-ordinates are (x, y). Thus each point in the plane is associated with a complex number. In the figure, P defines Z = x + iy. I..

Since every complex number z = x + iy is an order pair of real numbers (x, y), it can therefore be represented by a point P(x,y) in the xy plane by taking the real part along the x-axis and the imaginary part along the y-axis. This representation of a co..

Two complex numbers are equal iff their corresponding real parts and imaginary parts are separately equal..

Summary - If x and y are any real numbers, then x+iy is called a complex number. In the complex number x+iy, the real numbers x and y are respectively called the real part and imaginary part of x+iy. Two complex numbers are said to be equa..

All the q-th roots of z lie on a circle centred at the origin O and having radius equal to the real, positive q t h root of r. One of them has amplitude q /q and others are uniformly spaced around the circle separated from others by an angle 2p ..