Difference between revisions of "Manuals/calci/IMPRODUCT"

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<div style="font-size:30px">'''IMPRODUCT(z1,z2,z3)'''</div><br/>
 
<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>z1,z2,z3</math> are the complex numbers of the form <math>a+ib</math>  
−
*<math>n</math> is the power value.
+
 
  
 
==Description==
 
==Description==
−
*This function gives the value of powers of complex number.
+
*This function gives the product of the complex numbers.  
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*DeMoivre's Theorem is a generalized formula to compute powers of a complex number in it's polar form.
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*In IMPRODUCT(z1,z2,z3,…),Where z1,z2,z3,... are the complex numbers is in the form of "a+ib".i.e.  
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*i'is the imaginary unit, <math>i=sqrt(-1</math>.
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*a&b are the real numbers.'i' imaginary unit .<math>i=sqrt(-1)</math>.
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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∈(is belongs to) (-Pi(),Pi()].  
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*The multiplication of two complex numbers is a complex number.
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*This formula is called DeMoivre's theorem of complex numbers.  
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*Let z1=a+ib and z2=c+id.
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*We can use COMPLEX function to convert  real and imaginary number in to a complex number.
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*Then the product of two complex number is <math>z1.z2=(a+ib)(c+id)=(ac-bd)+(ad+bc)i</math> .  
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*In IMPOWER(z,n), n can be integer, fractional or negative.
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*In this function z1 is required.z2,z3,..., are optional.  
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*suppose n is nonnumeric , this function will returns the error value.
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*We can use COMPLEX function to convert  real and imaginary number in to a complex number.
  
 
==Examples==
 
==Examples==
  
−
#IMPOWER("4+5i",3)=-235.99999+115i
+
IMPRODUCT("1+3i","5+2i")=-1+17i
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#IMPOWER("9-7i",4)=-14852-8063.999999i
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IMPRODUCT("i","3-i")=1+3i
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#IMPOWER("6",9)=10077696(EXCEL)=10077696-8i(CALCI)
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IMPRODUCT("5","-2+4i")=-10+20i
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#IMPOWER("i",10)=-1-16i(CALCI)=-1+6.1257422745431E-16i
+
IMPRODUCT("2+3i","4+6i","3+5i")=-150+22i(EXCEL)=-10+24i(CALCI)
 +
IMPRODUCT("-6-2i","-1-i")=4+8i
  
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*For imaginary value '0' is not accepting in CALCI.
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*CALCI is not taking the third value for multiplication.
 +
*It only applied for two numbers
  
 
==See Also==
 
==See Also==

Revision as of 06:11, 17 December 2013

IMPRODUCT(z1,z2,z3)


  • are the complex numbers of the form


Description

  • This function gives the product of the complex numbers.
  • In IMPRODUCT(z1,z2,z3,…),Where z1,z2,z3,... are the complex numbers is in the form of "a+ib".i.e.
  • a&b are the real numbers.'i' imaginary unit ..
  • The multiplication of two complex numbers is a complex number.
  • Let z1=a+ib and z2=c+id.
  • Then the product of two complex number is .
  • In this function z1 is required.z2,z3,..., are optional.
  • We can use COMPLEX function to convert real and imaginary number in to a complex number.

Examples

IMPRODUCT("1+3i","5+2i")=-1+17i IMPRODUCT("i","3-i")=1+3i IMPRODUCT("5","-2+4i")=-10+20i IMPRODUCT("2+3i","4+6i","3+5i")=-150+22i(EXCEL)=-10+24i(CALCI) IMPRODUCT("-6-2i","-1-i")=4+8i

  • CALCI is not taking the third value for multiplication.
  • It only applied for two numbers

See Also


References

Binary Logarithm

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