Difference between revisions of "Manuals/calci/IMPRODUCT"
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==Description== | ==Description== | ||
*This function gives the product of the complex numbers. | *This function gives the product of the complex numbers. | ||
| − | *In IMPRODUCT(z1,z2,z3,…), | + | *In IMPRODUCT(z1,z2,z3,…), where z1,z2,z3,... are the complex numbers and is in the form of <math>a+ib</math>. |
| − | *where a&b are the real numbers. | + | *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 z1=a+ib and z2=c+id. | + | *Let <math>z1=a+ib</math> and <math>z2=c+id</math>. |
*Then the product of two complex number is <math>z1.z2=(a+ib)(c+id)=(ac-bd)+(ad+bc)i</math> . | *Then the product of two complex number is <math>z1.z2=(a+ib)(c+id)=(ac-bd)+(ad+bc)i</math> . | ||
| − | *In this function z1 is required.z2,z3,... | + | *In this function <math>z1</math> is required. <math>z2,z3,...</math> are optional. |
*We can use COMPLEX function to convert real and imaginary number in to a complex number. | *We can use COMPLEX function to convert real and imaginary number in to a complex number. | ||
| − | |||
==Examples== | ==Examples== | ||
Revision as of 23:33, 18 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
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} & 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 b} 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 .
- 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.
.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
See Also