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Difference between revisions of "Manuals/calci/COMPLEX"
 
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<div style="font-size:30px">'''COMPLEX(real,imaginary,suffix)'''</div><br/>
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<div style="font-size:30px">'''COMPLEX (Real,Imaginary,Suffix)'''</div><br/>
  
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*<math>real</math> is the real part of the complex number.
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*<math>Real</math> is the real part of the complex number.
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*<math>imaginary</math> is the imaginary part of the complex number.
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*<math>Imaginary</math> is the imaginary part of the complex number.
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*<math>suffix</math> is the imaginary unit of the complex number.
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*<math>Suffix</math> is the imaginary unit of the complex number.
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**COMPLEX(), converts real and imaginary coefficients into a complex number.
  
 
==Description==
 
==Description==
 +
 
*COMPLEX function converts the real and imaginary coefficients into a complex number.
 
*COMPLEX function converts the real and imaginary coefficients into a complex number.
 
*A complex number is a combination of a real and an imaginary number.
 
*A complex number is a combination of a real and an imaginary number.
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*For e.g. <math>{-4}^2 =16</math>. Because a negative times a negative is positive.
 
*For e.g. <math>{-4}^2 =16</math>. Because a negative times a negative is positive.
 
*A complex number is a number is  in the form <math> z = a + bi</math>, where <math>a</math> and <math>b</math> are real numbers and <math>i</math> is the imaginary unit. Where <math>i=\sqrt{-1}</math>
 
*A complex number is a number is  in the form <math> z = a + bi</math>, where <math>a</math> and <math>b</math> are real numbers and <math>i</math> is the imaginary unit. Where <math>i=\sqrt{-1}</math>
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*In <math>COMPLEX(real,imaginary,suffix)</math>, here <math>real</math> is the real part of the complex number, <math>imaginary</math> is the imaginary part of the complex number and <math>suffix</math> is the imaginary unit of a complex number like <math>i</math> or <math>j</math>.
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*In <math>COMPLEX(Real,Imaginary,Suffix)</math>, here <math>Real</math> is the real part of the complex number, <math>Imaginary</math> is the imaginary part of the complex number and <math>Suffix</math> is the imaginary unit of a complex number like <math>i</math> or <math>j</math>.
 
*To mention <math>i</math> and <math>j</math>, we must use the lower case only
 
*To mention <math>i</math> and <math>j</math>, we must use the lower case only
 
*In a complex number <math>z</math> real part is denoted by <math>Re(z)</math> & imaginary part is denoted by <math>Im(z)</math>.
 
*In a complex number <math>z</math> real part is denoted by <math>Re(z)</math> & imaginary part is denoted by <math>Im(z)</math>.
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*COMPLEX returns the error value, when <math>real</math> and <math>imaginary</math> are non-numeric.
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*COMPLEX returns the error value, when <math>Real</math> and <math>Imaginary</math> are non-numeric.
 
*<math>Suffix</math> should be either <math>i</math> or <math>j</math>, otherwise it shows error value.
 
*<math>Suffix</math> should be either <math>i</math> or <math>j</math>, otherwise it shows error value.
 
*A Complex number whose real part is zero is said to be purely imaginary.
 
*A Complex number whose real part is zero is said to be purely imaginary.
 
*A Complex number whose imaginary part is zero is a real number. In that cases we have to assign '0' for that part.  
 
*A Complex number whose imaginary part is zero is a real number. In that cases we have to assign '0' for that part.  
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**<math>=COMPLEX(5,2)</math> gives <math>5+2i</math>
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**COMPLEX(5,2) gives <math>5+2i</math>
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**<math>=COMPLEX(5,2,"j")</math> gives <math>5+2j</math>
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**COMPLEX(5,2,"j") gives <math>5+2j</math>
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 +
==ZOS==
  
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==ZOS Section==
 
 
*The syntax is to calculate COMPLEX in ZOS is <math>COMPLEX(REAL,IMAGINARY,SUFFIX)</math>
 
*The syntax is to calculate COMPLEX in ZOS is <math>COMPLEX(REAL,IMAGINARY,SUFFIX)</math>
 
*<math>REAL</math> is the real part.
 
*<math>REAL</math> is the real part.
 
*<math>IMAGINARY</math> is the imaginary part.
 
*<math>IMAGINARY</math> is the imaginary part.
 
*<math>SUFFIX</math> is imaginary unit which is either "i" or "j".
 
*<math>SUFFIX</math> is imaginary unit which is either "i" or "j".
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*E.x: COMPLEX(-1..1,10..11,"j")  
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*E.x: COMPLEX(-1..1,10..11,"j")
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{{#ev:youtube|N9v1byHycgs|280|center|Complex Number}}
  
 
==Examples==
 
==Examples==
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{| id="TABLE3" class="SpreadSheet blue"
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{| class="wikitable"
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|- class="even"
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|+Spreadsheet
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| Complex(real,imaginary,suffix)
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|-
 +
| COMPLEX(real,imaginary,suffix)
 
! rn
 
! rn
 
! in
 
! in
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|-
 
|-
 
|- class="odd"
 
|- class="odd"
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|Complex(5,6)
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|COMPLEX(5,6)
 
|5
 
|5
 
|6
 
|6
 
|
 
|
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|5+6i
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|       5+6i
 
|- class="even"
 
|- class="even"
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|Complex(5,2,"j")
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|COMPLEX(5,2,"j")
 
|5
 
|5
 
|2
 
|2
 
|j
 
|j
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|5+2j
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|         5+2j
 
|- class="odd"
 
|- class="odd"
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| Complex(2,0,"i")
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|COMPLEX(2,0,"i")
 
|2                                       
 
|2                                       
 
|0
 
|0
 
|i
 
|i
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|2
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|         2+0i
 
|- class="even"
 
|- class="even"
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| Complex(0,-4,i)
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|COMPLEX(0,-4,"i")
 
|0
 
|0
 
| -4
 
| -4
 
|i
 
|i
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| -4i
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|         0 + -4i
 
|- class="odd"
 
|- class="odd"
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|Complex(5,"j")
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|COMPLEX(5,"j")
 
|5
 
|5
 
|
 
|
 
|j
 
|j
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|Error
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| #N/A (INVALID IMAGINARY COEFFICIENTS)
 
|}
 
|}
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 +
==Related Videos==
 +
 +
{{#ev:youtube|SP-YJe7Vldo|280|center|Complex Numbers}}
  
 
==See Also==
 
==See Also==
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==References==
 
==References==
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[http://en.wikipedia.org/wiki/Complex_number  Complex Numbers]
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*[http://en.wikipedia.org/wiki/Complex_number  Complex Numbers]
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 +
 
 +
 
 +
 
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*[[Z_API_Functions | List of Main Z Functions]]
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 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 03:43, 12 October 2020

COMPLEX (Real,Imaginary,Suffix)


  • 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 Real} is the real part of the complex number.
  • 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 Imaginary} is the imaginary part of the complex number.
  • 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 Suffix} is the imaginary unit of the complex number.
    • COMPLEX(), converts real and imaginary coefficients into a complex number.

Description

  • COMPLEX function converts the real and imaginary coefficients into a complex number.
  • A complex number is a combination of a real and an imaginary number.
  • A number which is positive or negative, rational or irrational or decimals are called real numbers.
  • An Imaginary number is a number that when squring it gives a negative result.
  • For e.g. 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 {-4}^2 =16} . Because a negative times a negative is positive.
  • A complex number is a number is in 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 z = a + bi} , 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} 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 b} are real numbers and   is the imaginary unit. 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 i=\sqrt{-1}}
  • In 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 COMPLEX(Real,Imaginary,Suffix)} , here 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 Real} is the real part of the complex number,   is the imaginary part of the complex number 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 Suffix} is the imaginary unit of a complex number like 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} or 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 j} .
  • To mention 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} and  , we must use the lower case only
  • In a complex number 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} real part is denoted 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 Re(z)} & imaginary part is denoted 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 Im(z)} .
  • COMPLEX returns the error value, when   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 Imaginary} are non-numeric.
  • 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 Suffix} should be either 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} or 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 j} , otherwise it shows error value.
  • A Complex number whose real part is zero is said to be purely imaginary.
  • A Complex number whose imaginary part is zero is a real number. In that cases we have to assign '0' for that part.
    • COMPLEX(5,2) gives 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 5+2i}
    • COMPLEX(5,2,"j") gives 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 5+2j}

ZOS

  • The syntax is to calculate COMPLEX 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 COMPLEX(REAL,IMAGINARY,SUFFIX)}
  • 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 REAL} is the real part.
  • 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 IMAGINARY} is the imaginary part.
  •   is imaginary unit which is either "i" or "j".
  • E.x: COMPLEX(-1..1,10..11,"j")
Complex Number

Examples

Spreadsheet
COMPLEX(real,imaginary,suffix) rn in sf RESULT
COMPLEX(5,6) 5 6 5+6i
COMPLEX(5,2,"j") 5 2 j 5+2j
COMPLEX(2,0,"i") 2 0 i 2+0i
COMPLEX(0,-4,"i") 0 -4 i 0 + -4i
COMPLEX(5,"j") 5 j #N/A (INVALID IMAGINARY COEFFICIENTS)

Related Videos

Complex Numbers

See Also

References



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