Manuals/calci/IMPOWER

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IMPOWER(z,n)


  • is the complex number is of the form
  • is the power value.

Description

  • This function gives the value of powers of complex number.
  • DeMoivre's Theorem is a generalized formula to compute powers of a complex number in it's polar form.
  • is the imaginary unit,
  • Then the power of a complex number is defined by

where and , Failed to parse (syntax error): {\displaystyle \theta∈(-\pi,\pi]} .

  • This formula is called DeMoivre's theorem of complex numbers.
  • We can use COMPLEX function to convert real and imaginary number in to a complex number.
  • In IMPOWER(z,n), can be integer, fractional or negative.
  • If is non-numeric, function will return error value.

Examples

  1. =IMPOWER("4+5i",3) = -235.99999+115i
  2. =IMPOWER("9-7i",4) = -14852-8063.999999i
  3. =IMPOWER("6",9) = 10077696
  4. =IMPOWER("i",10) = -1+6.1257422745431E-16i

See Also

References

De Moivre's formula