By Kardi Teknomo, PhD .
ComplexNumber


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If Complex Number Tutorial: Complex Power is a complex number and Complex Number Tutorial: Complex Power is a natural number, then we can take the power of complex number is a complex number and Complex Number Tutorial: Complex Power is a natural number, then we can take the power of complex number is a natural number, then we can take the power of complex number

Complex Number Tutorial: Complex Power

Complex Number Tutorial: Complex Power

Complex Number Tutorial: Complex Power

Properties of Complex Power

  • The magnitude is Complex Number Tutorial: Complex Power
  • The direction is Complex Number Tutorial: Complex Power . Note the argument of the results must be reduced mod Complex Number Tutorial: Complex Power . Note the argument of the results must be reduced mod Complex Number Tutorial: Complex Power
  • De Moivre formula: Complex Number Tutorial: Complex Power for n as positive or negative integer. Some authors will make brief function Complex Number Tutorial: Complex Power , such that De Moivre formula becomes Complex Number Tutorial: Complex Power . for n as positive or negative integer. Some authors will make brief function Complex Number Tutorial: Complex Power , such that De Moivre formula becomes Complex Number Tutorial: Complex Power . , such that De Moivre formula becomes Complex Number Tutorial: Complex Power .
  • Parallelogram equality Complex Number Tutorial: Complex Power

More general case, if we have two complex numbers Complex Number Tutorial: Complex Power and Complex Number Tutorial: Complex Power , then we can take the power of complex number and Complex Number Tutorial: Complex Power , then we can take the power of complex number , then we can take the power of complex number

Complex Number Tutorial: Complex Power

Complex Number Tutorial: Complex Power

See Also : Complex Exponent , Complex Root , Complex Logarithm

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