What is complex plain and examples of it
The term you may be referring to is "complex plane," also known as the "Argand plane" or "Gauss plane." The complex plane is a two-dimensional Cartesian coordinate system where the coordinates of each point consist of a real number (horizontal axis) and an imaginary number (vertical axis). It provides a visual representation of complex numbers and their operations.
The complex plane can be represented as follows:
| Imaginary Axis (vertical)
|
|
|
|____________________
Real Axis (horizontal)
Here are a few examples of points plotted on the complex plane:
1. The point (3 + 2i) represents a complex number with a real part of 3 and an imaginary part of 2. This point would be located three units to the right on the real axis and two units up on the imaginary axis.
2. The point (-1 - 4i) represents a complex number with a real part of -1 and an imaginary part of -4. This point would be located one unit to the left on the real axis and four units down on the imaginary axis.
3. The point (2 - i) represents a complex number with a real part of 2 and an imaginary part of -1. This point would be located two units to the right on the real axis and one unit down on the imaginary axis.
These are just a few examples, but in the complex plane, any complex number can be represented by a point with a corresponding real and imaginary part.
The term "complex plane" refers to the coordinate system used to represent complex numbers graphically. It consists of a two-dimensional plane with a horizontal axis representing the real part of a complex number and a vertical axis representing the imaginary part.
A complex number is written in the form a + bi, where "a" is the real part and "b" is the imaginary part. Here are a few examples of complex numbers:
1. 2 + 3i: Here, 2 is the real part, and 3 is the imaginary part. It would be graphed as a point on the complex plane with coordinates (2, 3).
2. -5 - 2i: In this case, -5 is the real part, and -2 is the imaginary part. The corresponding point on the complex plane would be (-5, -2).
3. 4i: This is a purely imaginary number, as it does not have a real part. It would be depicted as the point (0, 4) on the complex plane.
4. -1: This is a real number, with no imaginary part. It would be represented by the point (-1, 0) on the complex plane.
In the complex plane, each complex number corresponds to a unique point, allowing for visualization and operations such as addition, subtraction, multiplication, and division.