Question

Is the Cartesian form the same as the rectangular form?

Answer 1

Hint: For solving these types of questions, firstly we need to understand these given terms by reading their definitions, by examining their graphs and also with the help of some examples. After understanding all the things related to these terms you will get your required answer.

Complete step by step answer:
A Cartesian coordinate system in two dimensions is also called a rectangular coordinate system. A Cartesian plane is a graph with one X axis and one Y axis. These two axes are perpendicular to each other. In the center of the graph there is origin. Numbers on the X axis that are on the right of the origin are positive and that are on the left of the origin are negative. Each point that is represented on the plane has a unique set of numbers, which is called as ordered pairs. The first number in the ordered pair will always be on the X axis portion and the second number in the ordered pair will always be on the Y axis portion.
Let’s see an example of a Cartesian plane representing several ordered pairs:

Rectangular form is used when we want to represent a complex number according to its Cartesian coordinates (it is used to represent \[z=a+bi\]), here the real part of the complex number lies on the X axis and the imaginary part lies on the Y axis. In rectangular form, a complex number is denoted by respective horizontal and vertical components. The horizontal component is referred to as the real component and the vertical component is referred to as the imaginary component.
Let’s understand it with more with the help of a figure:

So from observing all the above things, we can say that the Cartesian form and rectangular form are two different names for the same system but cartesian form is for representing real numbers and rectangular form is for complex numbers.
When we represent a complex number \[z=a+bi\] in Cartesian form it is called a rectangular form.

Note: The name Cartesian comes from the French mathematician who worked to merge algebra and Euclidean geometry. Cartesian coordinates tools are applied in geometry, astronomy, physics, engineering, computer graphics, data processing and many more all new 3D discoveries are related to this system.