Fundamental Mathematics/Arithmetic/Arithmetic Number/Complex Number

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Complex Number[edit]

Complex conjugate picture.svg

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]