Fundamental Mathematics/Arithmetic/Arithmetic Number/Complex Number

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Complex Number[edit | edit source]

Complex conjugate picture.svg

Complex Number

Complex conjugate Number

Mathematical Operations[edit | edit source]

Operation on 2 different complex numbers[edit | edit source]

Addition
Subtraction
Multilication
Division


Operation on complex numbers and its conjugate[edit | edit source]

Addition
Subtraction
Multilication
Division

In Polar form

Power of Z[edit | edit source]

Since

Hence


Since

Hence

Euler's formula[edit | edit source]

Euler formula[edit | edit source]


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 | edit source]


for any real and integer . This result is known as

Reference[edit | edit source]