Difference between revisions of "Manuals/calci/IMPRODUCT"
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*This function gives the product of the complex numbers. | *This function gives the product of the complex numbers. | ||
*In IMPRODUCT(z1,z2,z3,…), where z1,z2,z3,... are the complex numbers and is in the form of <math>a+ib</math>. | *In IMPRODUCT(z1,z2,z3,…), where z1,z2,z3,... are the complex numbers and is in the form of <math>a+ib</math>. | ||
| − | *where <math>a</math> & <math>b</math> are the real numbers.<math>i</math>is the imaginary unit .<math>i=\sqrt{-1}</math>. | + | *where <math>a</math> & <math>b</math> are the real numbers. <math>i</math> is the imaginary unit .<math>i=\sqrt{-1}</math>. |
*The multiplication of two complex numbers is a complex number. | *The multiplication of two complex numbers is a complex number. | ||
*Let <math>z1=a+ib</math> and <math>z2=c+id</math>. | *Let <math>z1=a+ib</math> and <math>z2=c+id</math>. | ||
Revision as of 00:12, 20 December 2013
IMPRODUCT(z1,z2,z3)
- 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 z1,z2,z3} are the complex numbers of the form 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 a+ib}
Description
- This function gives the product of the complex numbers.
- In IMPRODUCT(z1,z2,z3,…), where z1,z2,z3,... are the complex numbers and is in the form of 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 a+ib} .
- where 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 a} & are the real numbers. 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 i} is the imaginary unit .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 i=\sqrt{-1}} .
- The multiplication of two complex numbers is a complex number.
- Let 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 z1=a+ib} 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 z2=c+id} .
- Then the product of two complex number is 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 z1.z2=(a+ib)(c+id)=(ac-bd)+(ad+bc)i} .
- In this function 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 z1} is required. 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 z2,z3,...} are optional.
- We can use COMPLEX function to convert real and imaginary number in to a complex number.
are the real numbers. 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 i}
is the imaginary unit .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 i=\sqrt{-1}}
.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
- =IMPRODUCT("-6-2i","-1-i") = 4+8i