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Complex numbers

1) Formula of Euler :

 

2) Module of a complex number to ib:

 

3) Argument of a complex number to ib:

 

4) cartesian Representation of a complex number :

 

5) trigonometrical Representation of a complex number :

 

6) exponential Representation of a complex number :

is clearly therefore that |and the q | = 1

 

7) Describe the module and the phase of the n° complex turning out from the product of 2 complex numbers :

The module is the product of the modules and the phase is the sum of is made.

 

8) Describe the module and the phase of the n° complex turning out from the relationship of 2 complex numbers :

The module is the relationship of the modules and the phase is the difference of is made.

 

9)  : | z |2

 

10)  : 2Re(z)

 

11)  : 2Im(z)

 

12) Calcolo of the root n-esima of a complex number :

It can easily be written in exponential shape where the module is worth rn while the argument is