How to Plot the number 4 + 2i on a Graph?
A complex number is a part of the number system in mathematics which contains both real and imaginary numbers. Or we can say that complex numbers are formed by combining two parts: one real part and the other part an imaginary one. The standard representation form of complex numbers is given by:
x + yi
Here, x is called the real part of complex numbers and y is the imaginary part of complex numbers accompanying ‘i’. At any given point of time, either x or y can be zero, having just one part that contributes to the formation of a complex number. Or we can say, complex numbers are thus any numbers represented in the form of x + yi, where x and y are real numbers and ‘i’ is iota satisfying i2 = -1, or i3 = -i.
Example:
(i) 5 + 10i
In the complex number, 5 is the real part and 10 is the imaginary part
(ii) 6 – 6i
In the complex number, 6 is the real part and -6 is the imaginary part
(iii) 4 + 5i
In the complex number, 4 is the real part and 5 is the imaginary part
Classification of Complex Numbers
Some of the types of complex numbers are:
- Zero complex number: Here, a = 0, b = 0, so z = 0 + i0. For example, 0.
- Purely real number: Here, a ≠ 0, b = 0, so z = a + i0. For example, 4, 8, 2.
- Purely imaginary number: Here, a = 0, b ≠ 0, so z = 0 + ib. For example, 8i, -1i, 6i.
- Imaginary number: Here, a ≠ 0, b ≠ 0, so z = a + ib. For example, 1 + 3i, 6 – 12i.
Complex Plane
As we know a complex number is a sum of real and imaginary numbers that is x + yi. So the complex number is also represented by a point(let say (x, y)) in the XY plane. So the plane in which the complex number is assigned its point is known as complex plane or argand plane. Here the x-axis represents the real number so it is also known as the real axis and Y-axis represents the imaginary number so it is also known as the imaginary axis. Hence the graphical representation is:
Plotting Complex Numbers on Graph
Let us learn how to plot complex numbers on the graph with the help of an example. In the below example, we are plotting a+bi complex number on the graph
Given: a+bi
Here, a is the real number and b is the imaginary number.
So, we can plot a+bi on the graph using the following steps:
Step 1: The complex number can be presented as coordinates (a, b).
Step 2: To plot this on the graph, we will move ‘a’ blocks on the real axis and ‘b’ blocks above on the imaginary axis.
Plotting 4+2i on Graph
Solution:
Given that 4+2i
Here, the complex number 4+2i is in the form of a+bi.
So, 4 is the real number and 2 is the imaginary number.
Now using the following steps we can create the graph of 4+2i:
Step 1: The complex number can be presented as co-ordinates (4, 2).
Step 2: To plot this on graph, we will move 4 blocks on the real axis and 2 blocks above on the imaginary axis.
Similar Questions
Question 1. Mention the coordinates that correspond to 10-2i.
Solution:
The corresponding co-ordinates to 10+2i are (10, 2)
Question 2. Plot the graph 4-4i.
Solution:
The corresponding coordinates to 4-4i are (4, -4).
The graphical representation of the given coordinates will be:
Question 3. Plot the graph 4+4i.
Solution:
The corresponding coordinates to 4+4i are (4, 4).
The graphical representation of the given coordinates will be:
Question 4. Real Axis and Imaginary Axis correspond to what axis when considered on the graph?
Solution:
X-axis corresponds to real axis and Y-axis corresponds to imaginary axis
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