# Calculation rectangular form into polar form of a complex numbers

After learning the complex numbers conversion software (I have given it for free, click Converting complex numbers), then how to compare the results of execution software's program with the manual calculation?

Here I will give an example of the manual calculation method to convert complex numbers rectangular form into polar form, with sample questions 30 + j25

Given the rectangular form:

y (

Completion:

r (

φ (

Then the polar form becomes:

r ∟ φ° = 39.05125 ∟ 39.80557°

See a picture below, the calculation above

Given the rectangular form:

30 + j25

x (*real*) = 30y (

*imaginary*) = 25Completion:

r (

*abs*) = √(x^{2}+ y^{2}) = √(30^{2}+ 25^{2})= 39.05125φ (

*angle*) = tan^{-1}(y/x) = tan^{-1}(25/30) = 39.80557Then the polar form becomes:

r ∟ φ° = 39.05125 ∟ 39.80557°

See a picture below, the calculation above

**Rectangular form into polar form**

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