Difference between revisions of "Manuals/calci/IMPRODUCT"
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| − | <div | + | <div style="font-size:30px">'''IMPRODUCT(z1,z2,z3)'''</div><br/> |
| + | *<math>z1,z2,z3</math> are the complex numbers of the form <math>a+ib</math> | ||
| + | *<math>n</math> 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, <math>i=sqrt(-1</math>. | ||
| + | *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∈(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== | |
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| − | + | #IMPOWER("4+5i",3)=-235.99999+115i | |
| + | #IMPOWER("9-7i",4)=-14852-8063.999999i | ||
| + | #IMPOWER("6",9)=10077696(EXCEL)=10077696-8i(CALCI) | ||
| + | #IMPOWER("i",10)=-1-16i(CALCI)=-1+6.1257422745431E-16i | ||
| − | + | *For imaginary value '0' is not accepting in CALCI. | |
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| − | |||
| − | + | ==See Also== | |
| + | *[[Manuals/calci/IMREAL | IMREAL ]] | ||
| + | *[[Manuals/calci/IMSUM | IMSUM ]] | ||
| + | *[[Manuals/calci/IMAGINARY | IMAGINARY ]] | ||
| + | *[[Manuals/calci/COMPLEX | COMPLEX ]] | ||
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| − | + | ==References== | |
| − | + | [http://en.wikipedia.org/wiki/Binary_logarithm Binary Logarithm] | |
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Revision as of 05:07, 17 December 2013
IMPRODUCT(z1,z2,z3)
- are the complex numbers of the form
- is the power value.
are the complex numbers 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 (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 (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.
.
and Failed to parse (syntax error): {\displaystyle θ=tan^-1(y/x)}
, θ∈(is belongs to) (-Pi(),Pi()].Examples
- IMPOWER("4+5i",3)=-235.99999+115i
- IMPOWER("9-7i",4)=-14852-8063.999999i
- IMPOWER("6",9)=10077696(EXCEL)=10077696-8i(CALCI)
- IMPOWER("i",10)=-1-16i(CALCI)=-1+6.1257422745431E-16i
- For imaginary value '0' is not accepting in CALCI.
See Also