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Basics of Rectangular and Polar form Conversions [Complex Numbers]

The complex number is a sum of real and imaginary part. Such number is of the form a + jb, where a is the real part and b is the imaginary part.

After reading this post you'll learn:

  1. What is rectangular form
  2. What is polar form
  3. How to perform conversion between them

Basics of rectangular form

In this notation, a two-dimensional XY plane is used. Real part a goes along the x-axis. Whereas the imaginary part b is along the y-axis. For example, the complex number 5 + 8j in the rectangular form is a dot:

Basics of Polar form

There is another way by which we can represent the complex numbers. A polar form uses the magnitude of the number as the length of line and the angle at which a number extends. For example the number 7 ∠ 40°.

How to convert between Polar and Rectangular form

As you observed that polar and rectangular form conversions are very easy. Likewise, the conversions are. You just need to use these equations and you are ready to go.
basics of rectangular to polar conversions

For the sake of practice, 5 different examples are provided here. 
Rectangular form Polar form
5 + 10j 11.18∠63.43°
13 + 19j 23.02∠55.61°
4 + 93j 93.08∠87.53°
10 + 30j 31.62∠71.56°
139 + 272j 305.45∠62.93°
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