- 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
Thursday, June 7, 2012
Complex Numbers - Geometric Representation
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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 unit.in 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).
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