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Complex numbers

• Complex number

Properties

• Complex absolute value
• Complex argument
• Complex conjugate
• Complex exponent
• Complex modulus
• Complex plane
• Extended complex plane
• Absolute square

Coordinate systems

• Cartesian coordinates
• Polar coordinates

Notations

• Algebraic form
• Matrix form
• Phasor form
• Trigonometric form

Principal values

• Principle value of an argument
• Principle value of a logarithm
• Principle n-th root

Arithmetic Operations

• Calculation rules for complex numbers

• Addition of complex numbers
• Multiplication of complex numbers
• Matrix multiplication
• Logarithm of a complex number
• Root of complex numbers

Applications

• De Moivre's formula
• Euler's formula
• Negative square

Particularities

• Special values
• Riemann sphere
• Unit circle
• Binomial theorem
• Holomorphic function
• Phasor

 

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