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.
  • i'is the imaginary unit,
  • Then the power of a complex number is defined by Failed to parse (syntax error): {\displaystyle (z)^n=(x+iy)^n=r^n*e^{inθ}=r^n(cosnθ+isinnθ)} where . and Failed to parse (syntax error): {\displaystyle θ=tan^-1(y/x)} , θ∈(is belongs to) (-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), n can be integer, fractional or negative.
  • suppose n is nonnumeric , this function will returns the error value.

Examples

  1. IMPOWER("4+5i",3)=-235.99999+115i
  2. IMPOWER("9-7i",4)=-14852-8063.999999i
  3. IMPOWER("6",9)=10077696(EXCEL)=10077696-8i(CALCI)
  4. IMPOWER("i",10)=-1-16i(CALCI)=-1+6.1257422745431E-16i
  • For imaginary value '0' is not accepting in CALCI.

See Also


References

Binary Logarithm