Thursday, June 7, 2012

Complex Numbers - Geometric Representation

  • A simple quadratic equation x² + 1 = 0 has no solution in the set of real numbers. The solution of such equations fall into the set of complex numbers(C).
  • The solutions of the above equation are given by x² = -1
  • This implies x = ± √-1. The positive square root of -1 is represented by i
  • For any two real numbers x and y , we can form a new number x + iy. This number is called complex number.
  • A complex number is denoted by a single letter z. In a complex number         z = x + iy , x is called Real Part Re(z) and y is called Imaginary Part Im(z).
  • Every complex number x + iy can be represented geometrically as a unique point P(x,y) in the xy plane.
  • X-axis is called the real axis (Re) and Y-axis is called the imaginary axis (Im).
  • The plane having a complex number assigned to each of its points is called the complex plane. This representation of complex numbers as points in the plane is known as argand diagram
This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

1 comment:

  1. A number whose square is less than or equal to zero is termed as an imaginary number. Let's take an example, √-5 is an imaginary number and its square is -5. An imaginary number can be written as a real number but multiplied by the imaginary a+bi complex number i is called the imaginary unit,in given expression "a" is the real part and b is the imaginary part of the complex number. The complex number can be identified with the point (a, b).