Difference between revisions of "Manuals/calci/IMPOWER"
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*Then the power of a complex number is defined by <math>(z)^n=(x+iy)^n=r^n*e^{inθ}=r^n(cosnθ+isinnθ)</math> where <math>r=\sqrt{x^2+y^2}</math>. and <math>θ=tan^-1(y/x)</math>, θ∈(-Pi(),Pi()]. | *Then the power of a complex number is defined by <math>(z)^n=(x+iy)^n=r^n*e^{inθ}=r^n(cosnθ+isinnθ)</math> where <math>r=\sqrt{x^2+y^2}</math>. and <math>θ=tan^-1(y/x)</math>, θ∈(-Pi(),Pi()]. | ||
*This formula is called DeMoivre's theorem of complex numbers. | *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. | + | *We can use [[Manuals/calci/COMPLEX| COMPLEX]] function to convert real and imaginary number in to a complex number. |
*In IMPOWER(z,n), n can be integer, fractional or negative. | *In IMPOWER(z,n), n can be integer, fractional or negative. | ||
*suppose n is nonnumeric , this function will returns the error value. | *suppose n is nonnumeric , this function will returns the error value. | ||
| Line 21: | Line 21: | ||
==See Also== | ==See Also== | ||
| − | |||
| − | |||
| − | |||
| + | *[[Manuals/calci/IMREAL | IMREAL ]] | ||
| + | *[[Manuals/calci/IMSUM | IMSUM ]] | ||
| + | *[[Manuals/calci/IMAGINARY | IMAGINARY ]] | ||
| + | *[[Manuals/calci/COMPLEX | COMPLEX ]] | ||
==References== | ==References== | ||
[http://en.wikipedia.org/wiki/Binary_logarithm Binary Logarithm] | [http://en.wikipedia.org/wiki/Binary_logarithm Binary Logarithm] | ||
Revision as of 02:51, 19 December 2013
IMPOWER(z,n)
- is the complex number is of the form
- is the power value.
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 (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle θ=tan^-1(y/x)} , θ∈(-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.
. and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle θ=tan^-1(y/x)}
, θ∈(-Pi(),Pi()].Examples
- IMPOWER("4+5i",3)=-235.99999+115i
- IMPOWER("9-7i",4)=-14852-8063.999999i
- IMPOWER("6",9)=10077696
- IMPOWER("i",10)=-1+6.1257422745431E-16i