Fundamental Mathematics/Arithmetic/Arithmetic Number/Complex Number

Complex Number edit

 

Complex Number

 

Complex conjugate Number

 

Mathematical Operations edit

Operation on 2 different complex numbers edit

Addition  
Subtraction  
Multilication  
Division  


Operation on complex numbers and its conjugate edit

Addition  
Subtraction  
Multilication  
Division  

In Polar form

 
 

Power of Z edit

Since

 

Hence

 


Since

 

Hence

 

Euler's formula edit

Euler formula edit

 

of which there is the famous case (for θ = π):

 

More generally,

 

Eucleur's power can be expressed as complex number

 

Hence, conjugate of the complex number

 

Adding complex number and its conjugate

 
 

Minus complex number and its conjugate

 
 

de Moivre's formula edit

 

for any real   and integer  . This result is known as

Reference edit