What is value of i in Complex Numbers?
We can use ‘i’ to represent real and complex numbers, here is a generalized representation:
z = a + ib
where
- a and b are real numbers
- ib denotes the complex part
If the number z is purely imaginary then x = 0 and if the number z is real then y = 0.
Geometrical Interpretation of i
Let us see how we can graphically represent a complex number in the complex plane:
Complex numbers in the complex plane
The number can be in one of the four quadrants depending on the sign of real numbers x and y. We know that a number can have a complex part and real part. The real part decides whether point lies on positive or negative side of x axis and at what distance from y-axis. In contrast, the complex part denotes whether point lies on positive or negative side of y axis and at what distance from x-axis. Let us see each case and the corresponding quadrant.
|
Quadrant |
X coordinate |
Y coordinate |
|---|---|---|
|
1st Quadrant |
positive |
positive |
|
2nd Quadrant |
negative |
positive |
|
3rd Quadrant |
negative |
negative |
|
4th Quadrant |
positive |
negative |
Value of i
The value of i is a fundamental concept in mathematics, particularly in the field of complex numbers. The field of mathematics not only depends on real numbers but also complex numbers which can be represented by the value ‘i’ known as iota.
In this article, we will study what is ‘i’ and what is the value of ‘i’. We will also see how we can use ‘i’ to represent a complex number. Some solved examples have also been provided to ensure a better understanding of the concept.