Difference between revisions of "Manuals/calci/IMDIV"
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| − | <div style="font-size:30px">'''IMDIV( | + | <div style="font-size:30px">'''IMDIV()'''</div><br/> |
| − | * | + | *Parameters are any complex numbers of the form of a+ib. |
| + | **IMDIV(),returns the quotient of two complex numbers | ||
==Description== | ==Description== | ||
| Line 6: | Line 7: | ||
*This function gives the division of two complex numbers. | *This function gives the division of two complex numbers. | ||
*This function used to remove the <math>i</math> (imaginary unit) from the denominator. | *This function used to remove the <math>i</math> (imaginary unit) from the denominator. | ||
| − | * | + | *The two Parameters are in the form of <math>a+ib</math> and <math>c+id</math>, where <math>a,b,c</math> & <math>d</math> are real numbers <math>i</math> is the imaginary unit, <math>i=\sqrt{-1}</math>. |
*Let z1 and z2 are the two Complex Numbers. | *Let z1 and z2 are the two Complex Numbers. | ||
*To do the division of complex number we have follow the steps: | *To do the division of complex number we have follow the steps: | ||
| Line 15: | Line 16: | ||
*To find the Conjugate of a Complex Number we can use the function [[Manuals/calci/IMCONJUGATE | IMCONJUGATE]]. | *To find the Conjugate of a Complex Number we can use the function [[Manuals/calci/IMCONJUGATE | IMCONJUGATE]]. | ||
| − | ==ZOS | + | ==ZOS== |
| − | *The syntax is to calculate the IMDIV in ZOS is <math>IMDIV( | + | *The syntax is to calculate the IMDIV in ZOS is <math>IMDIV()</math>. |
| − | ** | + | **Parameters are any complex numbers of the form of a+ib. |
*For e.g.,IMDIV("3+2i","3-2i") | *For e.g.,IMDIV("3+2i","3-2i") | ||
| + | |||
| + | {{#ev:youtube|2I89nee0Gmc|280|center|ImDiv}} | ||
==Examples== | ==Examples== | ||
| − | #IMDIV("4+2i","3-i") =<math>\frac{4+2i}{3-i}*\frac{3+i}{3+i}</math> = <math>\frac{12+10i+2i^2}{3^2-i^2} = 10+\frac{10i}{10}</math> (because <math>i^2=-1</math>) = <math> 1+\frac{i}{1} = 1+ | + | #IMDIV("4+2i","3-i") =<math>\frac{4+2i}{3-i}*\frac{3+i}{3+i}</math> = <math>\frac{12+10i+2i^2}{3^2-i^2} = 10+\frac{10i}{10}</math> (because <math>i^2=-1</math>) = <math> 1+\frac{i}{1} = 1+1i </math> |
| − | #IMDIV("3-5i,2-6i") = 0.9+0.2i | + | #IMDIV("3-5i","2-6i") = 0.9+0.2i |
| − | #IMDIV("5","2+3i") = 0. | + | #IMDIV("5","2+3i") = 0.7692307692307693 + -1.1538461538461537i |
#IMDIV("1+i","2") = 0.5+0.5i | #IMDIV("1+i","2") = 0.5+0.5i | ||
| + | |||
| + | ==Related Videos== | ||
| + | |||
| + | {{#ev:youtube|Z8j5RDOibV4|280|center|Dividing Complex Numbers}} | ||
==See Also== | ==See Also== | ||
| Line 34: | Line 41: | ||
==References== | ==References== | ||
[http://en.wikipedia.org/wiki/Complex_division Complex Division] | [http://en.wikipedia.org/wiki/Complex_division Complex Division] | ||
| + | |||
| + | |||
| + | |||
| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | |||
| + | *[[ Z3 | Z3 home ]] | ||
Latest revision as of 15:34, 19 July 2018
IMDIV()
- Parameters are any complex numbers of the form of a+ib.
- IMDIV(),returns the quotient of two complex numbers
Description
- This function gives the division of two complex numbers.
- This function used to remove the 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} (imaginary unit) from the denominator.
- The two Parameters are 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} 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 c+id} , 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,b,c} & 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 d} are 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}} .
- Let z1 and z2 are the two Complex Numbers.
- To do the division of complex number we have follow the steps:
step 1: Write the complex number in the fraction form. step 2: Find the conjugate of the denominator. step 3: Multiply the numerator and denominator with conjugate.
- 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 IMDIV(z1,z2) = \frac{a+ib}{c+id} = \frac{a+ib}{c+id}*\frac{c-id}{c-id} =\frac{ac+bd}{c^2+d^2}+\frac{(bc-ad)i}{(c^2+d^2)}} .
- To find the Conjugate of a Complex Number we can use the function IMCONJUGATE.
ZOS
- The syntax is to calculate the IMDIV in ZOS 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 IMDIV()}
.
- Parameters are any complex numbers of the form of a+ib.
- For e.g.,IMDIV("3+2i","3-2i")
Examples
- IMDIV("4+2i","3-i") =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 \frac{4+2i}{3-i}*\frac{3+i}{3+i}} = 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 \frac{12+10i+2i^2}{3^2-i^2} = 10+\frac{10i}{10}} (because 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^2=-1} ) =
- IMDIV("3-5i","2-6i") = 0.9+0.2i
- IMDIV("5","2+3i") = 0.7692307692307693 + -1.1538461538461537i
- IMDIV("1+i","2") = 0.5+0.5i
Related Videos
See Also
References