- Books Name
- AMARENDRA PATTANAYAK Mathmatics Book
- Publication
- KRISHNA PUBLICATIONS
- Course
- CBSE Class 11
- Subject
- Mathmatics
Chapter 5
Complex Numbers and Quadratic Equations
Imaginary Numbers and Powers
It is a solution to the quadratic equation or expression, x2+1 = 0, such as;
x2 = 0 – 1
x2 = -1
x = √-1
x = i
Therefore, an imaginary number is the part of complex number which we can write like a real number multiplied by the imaginary unit i, where i2 = -1. The imaginary number, when multiplied by itself, gives a negative value.
Value of Powers of i
We know, i2 = -1, let us calculate the value of ‘i’ raised to the power other imaginary numbers.
i4n = 1
i4n+1 = i
i4n+2= -1
i4n+3=-i